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## CURRENTLY DISPLAYING:

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## Distributive semigroup rings and related topics

### Journal of Mathematical Sciences (1999-05-01) 94: 1888-1924 , May 01, 1999

## Endomorphism Rings of Abelian Groups

### Journal of Mathematical Sciences (2002-06-01) 110: 2683-2745 , June 01, 2002

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

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

## 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 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.

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

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

## 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.

## 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} $
.

## 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.

## 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.

## 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

## 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.

## Plane modules and distributive rings

### Ukrainian Mathematical Journal (1993-05-01) 45: 794-797 , May 01, 1993

Let*A* be a semiprime ring entire over its center. We prove that the following conditions are equivalent: (a) A is a ring distributive from the right (left); (b) w.gl. dim (A) ≤ 1; moreover, if*M* is an arbitrary prime ideal of the ring*A*, then*A/M* is a right Ore set.

## 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.

## Primitively pure submodules and primitively divisible modules

### Journal of Mathematical Sciences (2002-06-01) 110: 2746-2754 , June 01, 2002

## Quaternion algebras over commutative rings

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

## Semi-chained rings and modules

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

## Structure of modules close to injective

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

## Endo - Distributive and Endo - Bezout Modules

### Groups, Rings, Lie and Hopf Algebras (2003-01-01) 555: 221-241 , January 01, 2003

This paper is a review of the author’s results on endo-distributive and endo - Bezout modules (some of the results are new).

## Left and right distributive rings

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

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*.

## Properties of endomorphism rings of Abelian groups, I

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

## 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.

## Distributive rings

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

## Distributive extensions of modules over noncommutative rings

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

## Semidistributive and distributively decomposable rings

### Mathematical Notes (1999-02-01) 65: 253-258 , February 01, 1999

A module is said to be distributive if the lattice of all its submodules is distributive. A module is called semidistributive if it is a direct sum of distributive modules. Right semidistributive rings, as well as distributively decomposable rings, are investigated.

## Semiinjective modules

### Mathematical notes of the Academy of Sciences of the USSR (1982-03-01) 31: 230-234 , March 01, 1982

## I

### Encyclopaedia of Mathematics (1995-01-01): 123-339 , January 01, 1995

The three-dimensional space that is the orbit space of the action of the binary icosahedron group on the three-dimensional sphere. It was discovered by H. Poincaré as an example of a homology sphere of genus 2 in the consideration of Heegaard diagrams (cf. *Heegaard diagram*).

## 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.

## Semihereditary rings and FP-injective modules

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

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

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

## 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.

## 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.

## 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.

## Rings of endomorphisms and distributivity

### Mathematical Notes (1994-10-01) 56: 1089-1096 , October 01, 1994

## On quaternion algebras

### Journal of Mathematical Sciences (1995-06-01) 75: 1750-1753 , June 01, 1995

It is proved that the distributiveness of the right ideals lattice for a quaternion algebra over a commutative ring A is equivalent to the following property: the equation x^{2}+y^{2}+z^{2}=0 is uniquely solvable in the field A/M for any maximal ideals M of A, the lattice of the ideals of A being distributive. Bibliography: 5 titles.

## 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

## Quasiprojective modules

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

## Polynomial and Series Rings and Principal Ideals

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

## 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.

## Semiregular, Weakly Regular, and Π-Regular Rings

### Journal of Mathematical Sciences (2002-04-01) 109: 1509-1588 , April 01, 2002

## 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.

## 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.

## 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.

## 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.

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

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

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