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## CURRENTLY DISPLAYING:

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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

## Properties of endomorphism rings of Abelian groups, I

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

## Modules over discrete valuation domains. I

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

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

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

## Modules in Which Sums or Intersections of Two Direct Summands Are Direct Summands

### Journal of Mathematical Sciences (2015-12-01) 211: 297-303 , December 01, 2015

This paper contains new characterizations of SSPm. odules, SIP-modules, D_{3}-modules, and C_{3}-modules. These characterizations are used for the proof of new and known results related to SSP-modules and SIP-modules. We also apply obtained results to endo-regular modules.

## Rings of Eventually Constant Sequences

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

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

### Journal of Mathematical Sciences (2010-06-01) 167: 868-869 , June 01, 2010

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

## Distributive rings

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

## Submodules and direct summands

### Journal of Mathematical Sciences (2009-12-15) 164: 1-20 , December 15, 2009

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

## Quasiprojective modules

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

## 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

## Bezout modules and rings

### Journal of Mathematical Sciences (2009-11-12) 163: 596-597 , November 12, 2009

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.

## Modules

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

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

## Modules over discrete valuation domains. II

### Journal of Mathematical Sciences (2008-06-01) 151: 3255-3371 , June 01, 2008

In the second part of the paper, we study torsion-free modules and mixed modules. We analyze the possibility of the isomorphism of two modules with isomorphic endomorphism rings. We touch on several questions about transitive and fully transitive modules.

## Modules with Nakayama’s property

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

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

## Multiplication modules and ideals

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

## Quaternion algebras over commutative rings

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

## Distributive semiprime rings

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

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

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.

## Formal Matrices and Their Determinants

### Journal of Mathematical Sciences (2015-12-01) 211: 341-380 , December 01, 2015

In the present paper, we study formal matrix rings over a given ring and determinants of such matrices.

## Nonreduced π-projective modules over hereditary rings

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

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

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

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

## Homomorphisms close to regular and their applications

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

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

## Semidistributive modules

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

## Flat modules and distributive rings

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

## Rings over which each module possesses a maximal submodule

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

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

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

## Structure of modules close to injective

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

## Distributively generated rings and distributive modules

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

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

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.

## Extensions of Automorphisms of Submodules

### Journal of Mathematical Sciences (2015-05-01) 206: 583-596 , May 01, 2015

We study modules *M* such that all automorphisms of submodules in *M* can be extended to endomorphisms (automorphisms) of *M*.

## Automorphism-Invariant Modules

### Journal of Mathematical Sciences (2015-05-01) 206: 694-698 , May 01, 2015

It is proved that all automorphism-invariant nonsingular right *A*-modules are injective if and only if the factor ring *A/G*(*A*_{A}) of the ring *A* with respect to the right Goldie radical *G*(*A*_{A}) is right strongly semiprime.

## Polynomial and Series Rings and Principal Ideals

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

## Distributive rings and modules

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

## Maximal submodules and locally perfect rings

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

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

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

## Modules with many direct summands

### Journal of Mathematical Sciences (2008-07-01) 152: 298-303 , July 01, 2008

We study rings over which all right modules are *I*_{0}-modules.

## Modules over formal matrix rings

### Journal of Mathematical Sciences (2010-11-01) 171: 248-295 , November 01, 2010

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

## Rings with projective principal right ideals

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

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

## Completely integrally closed modules and rings. III

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

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

## Retractable and Coretractable Modules

### Journal of Mathematical Sciences (2016-02-01) 213: 132-142 , February 01, 2016

In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and their interrelations. Right fully Kasch rings are described. It is proved that for a module *M* of finite length, the following conditions are equivalent. (1) In the category *σ*(*M*), every module is retractable. (2) In the category *σ*(*M*), every module is coretractable. (3) *M* is a CSL-module. (4) Ext
_{R}^{1}
(*S*_{1}*, S*_{2}) = 0 for any two simple nonisomorphic modules *S*_{1}*, S*_{2} ∈ *σ*(*M*). (5) *M* is a fully Kasch module.