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## Semi-chained rings and modules

### Mathematical Notes of the Academy of Sciences of the USSR (1990-08-01) 48: 781-786 , August 01, 1990

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## Properties of endomorphism rings of Abelian groups, I

### Journal of Mathematical Sciences (2002-12-01) 112: 4598-4735 , December 01, 2002

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## Modules over discrete valuation domains. I

### Journal of Mathematical Sciences (2007-09-01) 145: 4997-5117 , September 01, 2007

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## Endomorphism rings, power series rings, and serial modules

### Journal of Mathematical Sciences (1999-12-01) 97: 4538-4654 , December 01, 1999

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## Rings of Eventually Constant Sequences

### Journal of Mathematical Sciences (2003-01-01) 113: 175-178 , January 01, 2003

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## Distributive rings

### Mathematical Notes of the Academy of Sciences of the USSR (1984-03-01) 35: 171-172 , March 01, 1984

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## Quasiprojective modules

### Siberian Mathematical Journal (1980-05-01) 21: 446-450 , May 01, 1980

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## Rings with flat right ideals and distributive rings

### Mathematical Notes of the Academy of Sciences of the USSR (1985-08-01) 38: 631-636 , August 01, 1985

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## Modules

### Journal of Soviet Mathematics (1983-12-01) 23: 2642-2707 , December 01, 1983

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A survey is given of results on modules over rings, covering 1976–1980 and continuing the series of surveys “Modules” in Itogi Nauki.

## Distributive rings of series

### Mathematical Notes of the Academy of Sciences of the USSR (1986-04-01) 39: 285-290 , April 01, 1986

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## Rings without infinite sets of noncentral orthogonal idempotents

### Journal of Mathematical Sciences (2009-10-26) 162: 730-739 , October 26, 2009

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Let *A* be a ring without infinite sets of noncentral orthogonal idempotents. *A* is an exchange ring if and only if all Pierce stalks of *A* are semiperfect rings. All *A*-modules are *I*_{0}-modules if and only if either *A* is a right semi-Artinian ring in which every proper right ideal is the intersection of maximal right ideals or *A*/ SI(*A*_{A}) is an Artinian serial ring such that the square of the Jacobson radical of *A*/ SI(*A*_{A}) is equal to zero.

## Modules with Nakayama’s property

### Journal of Mathematical Sciences (2013-09-01) 193: 601-605 , September 01, 2013

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Modules *M*_{A} with Nakayama’s property are studied. In particular, for a right invariant ring *A*, it is proved that all right *A*-modules satisfy Nakayama’s property if and only if the ring *A* is right perfect.

## Semihereditary rings and FP-injective modules

### Journal of Mathematical Sciences (2002-12-01) 112: 4736-4742 , December 01, 2002

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## A remark on the intersection of powers of the Jacobson radical

### Journal of Mathematical Sciences (2010-06-22) 167: 868-869 , June 22, 2010

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If *A* is a left Noetherian, right distributive ring, then
$ \bigcap\limits_{k = 1}^\infty {{{\left( {J(A)} \right)}^k} = 0} $
.

## The Jacobson radical of the Laurent series ring

### Journal of Mathematical Sciences (2008-02-01) 149: 1182-1186 , February 01, 2008

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For a large class of rings *A*, including all rings with right Krull dimension, it is proved that for every automorphism ϕ of the ring *A*, the Jacobson radical of the skew Laurent series ring *A*((*x*, ϕ)) is nilpotent and coincides with *N*((*x*, ϕ)), where *N* is the prime radical of the ring *A*. If *A/N* is a ring of bounded index, then the Jacobson radical of the Laurent series ring *A*((*x*)) coincides with *N*((*x*)).

## Multiplication modules and ideals

### Journal of Mathematical Sciences (2006-07-01) 136: 4116-4130 , July 01, 2006

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## Quaternion algebras over commutative rings

### Mathematical Notes (1993-02-01) 53: 204-207 , February 01, 1993

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## Distributive semiprime rings

### Mathematical Notes (1995-11-01) 58: 1197-1215 , November 01, 1995

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It is proved that a right distributive semiprime PI ring*A* is a left distributive ring and for each element*x* ∈*A* there is a positive integer*n* such that*x*^{n}*A*=*Ax*^{n}. We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive left Noetherian PI rings. We also characterize rings all of whose Pierce stalks are right chain right Artin rings.

## Flat modules and rings finitely generated as modules over their center

### Mathematical Notes (1996-08-01) 60: 186-203 , August 01, 1996

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A module is called distributive (is said to be a chain module) if the lattice of all its submodules is distributive (is a chain). Let a ring*A* be a finitely generated module over its unitary central subring*R*. We prove the equivalence of the following conditions:
(1)

*A* is a right or left distributive semiprime ring;

for any maximal ideal*M* of a subring*R* central in*A*, the ring of quotients*A*_{M} is a finite direct product of semihereditary Bézout domains whose quotient rings by the Jacobson radicals are finite direct products of skew fields;

all right ideals and all left ideals of the ring*A* are flat (right and left) modules over the ring*A*, and*A* is a distributive ring, without nonzero nilpotent elements, all of whose quotient rings by prime ideals are semihereditary orders in skew fields.

## Nonreduced π-projective modules over hereditary rings

### Journal of Mathematical Sciences (2000-12-01) 102: 4671-4677 , December 01, 2000

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## Rings over which all modules are I 0-modules

### Journal of Mathematical Sciences (2009-01-09) 156: 336-341 , January 09, 2009

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Let *A* be a ring that does not contain an infinite set of idempotents that are orthogonal modulo the ideal SI(*A*_{A}). It is proved that all *A*-modules are *I*_{0}-modules if and only if either *A* is a right semi-Artinian, right V-ring or *A*/SI(*A*_{A}) is an Artinian serial ring and the square of the Jacobson radical of *A*/SI(*A*_{A}) isequal to zero.

## Distributive Rings, Uniserial Rings of Fractions, and Endo-Bezout Modules

### Journal of Mathematical Sciences (2003-03-01) 114: 1185-1203 , March 01, 2003

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## Homomorphisms close to regular and their applications

### Journal of Mathematical Sciences (2012-06-01) 183: 275-298 , June 01, 2012

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This paper contains new and known results on homomorphisms that are close to regular. The main results are presented with proofs.

## Distributive extensions of modules over noncommutative rings

### Journal of Mathematical Sciences (2007-06-01) 143: 3509-3516 , June 01, 2007

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## Semidistributive modules

### Journal of Mathematical Sciences (1999-05-01) 94: 1809-1887 , May 01, 1999

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## Flat modules and distributive rings

### Journal of Mathematical Sciences (1999-07-01) 95: 2421-2462 , July 01, 1999

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## Rings over which each module possesses a maximal submodule

### Mathematical Notes (1997-03-01) 61: 333-339 , March 01, 1997

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Right Bass rings are investigated, that is, rings over which any nonzero right module has a maximal submodule. In particular, it is proved that if any prime quotient ring of a ring*A* is algebraic over its center, then*A* is a right perfect ring iff*A* is a right Bass ring that contains no infinite set of orthogonal idempotents.

## Modules over Endomorphism Rings

### Mathematical Notes (2004-05-01) 75: 836-847 , May 01, 2004

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It is proved that *A* is a right distributive ring if and only if all quasiinjective right *A*-modules are Bezout left modules over their endomorphism rings if and only if for any quasiinjective right *A*-module *M* which is a Bezout left End *(M)*-module, every direct summand *N* of *M* is a Bezout left End*(N)*-module. If *A* is a right or left perfect ring, then all right *A*-modules are Bezout left modules over their endomorphism rings if and only if all right *A*-modules are distributive left modules over their endomorphism rings if and only if *A* is a distributive ring.

## Distributive rings and endodistributive modules

### Ukrainian Mathematical Journal (1986-01-01) 38: 54-58 , January 01, 1986

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## Structure of modules close to injective

### Siberian Mathematical Journal (1977-07-01) 18: 631-637 , July 01, 1977

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## Distributively generated rings and distributive modules

### Mathematical Notes (2000-10-01) 68: 488-495 , October 01, 2000

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A module is said to be distributively generated if it is generated by distributive submodules. We prove that the endomorphism ring of a finitely generated projective right module over a right distributively generated ring is a right distributively generated ring. If*M* is a module over a ring*A* and*A/J(A)* is a normal exchange ring, then*M* is a distributive module⇔*M* is a Bezout module.

## The Structure of Modules over Hereditary Rings

### Mathematical Notes (2000-11-01) 68: 627-639 , November 01, 2000

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Let *A* be a bounded hereditary Noetherian prime ring. For an *A*-module *M*_{A}, we prove that *M* is a finitely generated projective
$${A \mathord{\left/ {\vphantom {A {r\left( M \right)}}} \right. \kern-\nulldelimiterspace} {r\left( M \right)}}$$
-module if and only if *M* is a
$${\pi }$$
-projective finite-dimensional module, and either *M* is a reduced module or *A* is a simple Artinian ring. The structure of torsion or mixed
$${\pi }$$
-projective *A*-modules is completely described.

## Polynomial and Series Rings and Principal Ideals

### Journal of Mathematical Sciences (2003-03-01) 114: 1204-1226 , March 01, 2003

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## Distributive rings and modules

### Mathematical Notes of the Academy of Sciences of the USSR (1990-02-01) 47: 199-206 , February 01, 1990

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## Maximal submodules and locally perfect rings

### Mathematical Notes (1998-07-01) 64: 116-120 , July 01, 1998

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Rings over which every nonzero right module has a maximal submodule are called*right Bass rings*. For a ring*A* module-finite over its center*C*, the equivalence of the following conditions is proved:
(1)

*A* is a tight Bass ring;

*A* is a left Bass ring;

*A/J(A)* is a regular ring, and*J(A)* is a right and left*t*-nilpotent ideal.

## Distributive and Multiplication Modules and Rings

### Mathematical Notes (2004-03-01) 75: 391-400 , March 01, 2004

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We study rings in which every ideal is a finitely generated multiplication right ideal.

## Rings over which all cyclic modules are poorly injective

### Journal of Soviet Mathematics (1986-05-01) 33: 1153-1157 , May 01, 1986

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## Submodules and direct summands

### Journal of Mathematical Sciences (2009-12-28) 164: 1-20 , December 28, 2009

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This paper contains new and known results on modules in which submodules are close to direct summands. The main results are presented with proofs.

## Modules over formal matrix rings

### Journal of Mathematical Sciences (2010-11-05) 171: 248-295 , November 05, 2010

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This work contains some new and known results on modules over formal matrix rings. The main results are presented with proofs.

## Rings over which all modules are semiregular

### Journal of Mathematical Sciences (2008-10-18) 154: 249-255 , October 18, 2008

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For a ring *A*, it is proved that all *A*-modules are semiregular if and only if *A* is an Artinian serial ring and *J*^{2}(*A*) = 0.

## Rings with projective principal right ideals

### Ukrainian Mathematical Journal (1990-06-01) 42: 760-762 , June 01, 1990

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It has been proved that if A is a right-distributive ring, algebraic over its center, and whose principal ideals are projective, then A is a left-distributive ring.

## Distributive monoid algebras

### Mathematical Notes (1992-02-01) 51: 177-182 , February 01, 1992

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## Completely integrally closed modules and rings. III

### Journal of Mathematical Sciences (2012-06-01) 183: 413-423 , June 01, 2012

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We study rings *A* over which all cyclic right modules are completely integrally closed. The complete answer is obtained if either *A* is a semiperfect ring or each ring direct factor of *A* that is a domain is right bounded.

## Flat and Multiplication Modules

### Journal of Mathematical Sciences (2005-07-01) 128: 2998-3004 , July 01, 2005

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## Distributive modules and rings and their close analogs

### Journal of Mathematical Sciences (1999-01-01) 93: 149-253 , January 01, 1999

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## Idempotent functors and localizations in categories of modules and Abelian groups

### Journal of Mathematical Sciences (2012-06-01) 183: 323-382 , June 01, 2012

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The present paper contains various results on idempotent functors and localizations in categories of modules and Abelian groups.

## Distributive and Semihereditary Rings

### Journal of Mathematical Sciences (2005-08-01) 128: 3496-3500 , August 01, 2005

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Let *A* be a right and left distributive ring. For a positive integer *n*, we obtain a criterion of projectivity of all *n*-generated right ideals of the ring *A* and a criterion of the right semi-heredity of the ring *A*.

## Nonreduced @pgr;-Projective Modules over Hereditary Rings

### Journal of Mathematical Sciences (2000-12-01) 102: 4672-4678 , December 01, 2000

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## Bezout modules and rings

### Journal of Mathematical Sciences (2009-11-24) 163: 596-597 , November 24, 2009

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For any ring *A*, there exist a Bezout ring *R* and an idempotent *e* ∈ *R* with *A* ≅ *eRe*. Every module over any ring is a direct summand of an endo-Bezout module. Over any ring, every free module of infinite rank is an endo-Bezout module.

## Left and right distributive rings

### Mathematical Notes (1995-10-01) 58: 1100-1116 , October 01, 1995

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By a distributive module we mean a module with a distributive lattice of submodules. Let*A* be a right distributive ring that is algebraic over its center and let*B* be the quotient ring of*A* by its prime radical*H*. Then*B* is a left distributive ring, and*H* coincides with the set of all nilpotent elements of*A*.