Communications in Algebra, ISSN 0092-7872, 05/2015, Volume 43, Issue 5, pp. 1742 - 1751

It is well known that every uniquely clean ring is strongly clean. In this article, we investigate the question of when this result holds element-wise. We...

Secondary 16D50, 16E50 | Strongly clean elements | Uniquely clean elements | Clean ring | Primary 16U99 | MATHEMATICS | Secondary 16D50 | 16E50

Secondary 16D50, 16E50 | Strongly clean elements | Uniquely clean elements | Clean ring | Primary 16U99 | MATHEMATICS | Secondary 16D50 | 16E50

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 04/2020, Volume 224, Issue 4, p. 106211

We define the rank of elements of general unital rings, discuss its properties and give several examples to support the definition. In semiprime rings we give...

Idempotent | Rank | Unit-regular element | Minimal right ideal | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Rings and Algebras

Idempotent | Rank | Unit-regular element | Minimal right ideal | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Rings and Algebras

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 4/2018, Volume 92, Issue 2, pp. 375 - 383

We shall use the minus partial order combined with Pierce’s decomposition to derive the class of outer inverses for idempotents, units and group invertible...

Outer inverses | Analysis | 16E50 | Mathematics | Invariance | Combinatorics | Regularity | 15A09 | Pierce decomposition | MATHEMATICS | MATHEMATICS, APPLIED

Outer inverses | Analysis | 16E50 | Mathematics | Invariance | Combinatorics | Regularity | 15A09 | Pierce decomposition | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 6/2019, Volume 93, Issue 3, pp. 587 - 600

Matrix equations involving a family of unknown matrices $$X_1, \ldots , X_k$$ X 1 , … , X k can be written in a general form $$f(X_1, \ldots , X_k) = 0$$ f ( X...

15A24 | Analysis | 16E50 | Mathematics | Invariance | Combinatorics | Identity | 15A09 | Matrix equation | Generalized inverse | 47A50 | Mathematical analysis | Nonlinear equations

15A24 | Analysis | 16E50 | Mathematics | Invariance | Combinatorics | Identity | 15A09 | Matrix equation | Generalized inverse | 47A50 | Mathematical analysis | Nonlinear equations

Journal Article

Mathematische Annalen, ISSN 0025-5831, 10/2017, Volume 369, Issue 1, pp. 397 - 439

We present a novel quantitative approach to the representation theory of finite dimensional algebras motivated by the emerging theory of graph limits. We...

Mathematics, general | Mathematics | 16G10 | 16E50 | MATHEMATICS | BOUNDED DEGREE GRAPHS | LIMITS | PROPERTY | Algebra | Algorithms

Mathematics, general | Mathematics | 16G10 | 16E50 | MATHEMATICS | BOUNDED DEGREE GRAPHS | LIMITS | PROPERTY | Algebra | Algorithms

Journal Article

Canadian Journal of Mathematics, ISSN 0008-414X, 10/2018, Volume 70, Issue 5, pp. 961 - 982

For a division ring D, denote by M-D the D-ring obtained as the completion of the direct limit lim(-> n) M(2)n (D) with respect to the metric induced by its...

Rank function | Completion | Von Neumann regular ring | Factor | Ultramatricial | rank function | MATHEMATICS | completion | ALGEBRAS | REGULAR-RINGS | von Neumann regular ring | ultramatricial | factor

Rank function | Completion | Von Neumann regular ring | Factor | Ultramatricial | rank function | MATHEMATICS | completion | ALGEBRAS | REGULAR-RINGS | von Neumann regular ring | ultramatricial | factor

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 10/2018, Volume 41, Issue 4, pp. 1835 - 1857

In this paper, we give new existence criteria for the inverse along an element by means of Drazin inverses, one-sided annihilator ideals, idempotents and...

Ring | 16E50 | 20M99 | Mathematics, general | Inverse along an element | Mathematics | Semigroup | Applications of Mathematics | Generalized inverse | 15A09 | CORE | MATHEMATICS | RINGS | GENERALIZED INVERSES

Ring | 16E50 | 20M99 | Mathematics, general | Inverse along an element | Mathematics | Semigroup | Applications of Mathematics | Generalized inverse | 15A09 | CORE | MATHEMATICS | RINGS | GENERALIZED INVERSES

Journal Article

Forum Mathematicum, ISSN 0933-7741, 01/2015, Volume 27, Issue 1, pp. 549 - 574

We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain...

Quiver | irreducible representation | left-infinite path | Leavitt path algebra | 16E50 | 16D90 | algebraic branching system | 16G20 | Left-infinite path | Irreducible representation | Algebraic branching system | ARBITRARY GRAPHS | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | SOCLE | CATEGORY | K-THEORY

Quiver | irreducible representation | left-infinite path | Leavitt path algebra | 16E50 | 16D90 | algebraic branching system | 16G20 | Left-infinite path | Irreducible representation | Algebraic branching system | ARBITRARY GRAPHS | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | SOCLE | CATEGORY | K-THEORY

Journal Article

Publicacions Matematiques, ISSN 0214-1493, 2018, Volume 62, Issue 1, pp. 253 - 284

For V a vector space over a field, or more generally, over a division ring, it is well-known that every x is an element of End(V) has an inner inverse; that...

Inner inverse to a ring element | Endomorphism ring of a vector space | Inverse monoid | MATHEMATICS | inner inverse to a ring element | inverse monoid

Inner inverse to a ring element | Endomorphism ring of a vector space | Inverse monoid | MATHEMATICS | inner inverse to a ring element | inverse monoid

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 05/2016, Volume 64, Issue 5, pp. 834 - 841

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring....

matrices over a ring | von Neumann regularity | inverse along an element | Green's relations | Green’s relations | MATHEMATICS | 16E50 | 15A09 | Inverse | Algebra | Criteria | Equivalence

matrices over a ring | von Neumann regularity | inverse along an element | Green's relations | Green’s relations | MATHEMATICS | 16E50 | 15A09 | Inverse | Algebra | Criteria | Equivalence

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 3/2019, Volume 42, Issue 2, pp. 569 - 583

In this paper, we investigate the class of von Neumann regular modules over commutative rings. More precisely, we introduce a characterization of regular...

13C13 | Mathematics | Semisimple module | 13C11 | 13C05 | Von Neumann regular ring | Regular module | 16D60 | Krull’s intersection theorem | 16E50 | 16D40 | Mathematics, general | Applications of Mathematics | Prime submodule | MATHEMATICS | Krull's intersection theorem

13C13 | Mathematics | Semisimple module | 13C11 | 13C05 | Von Neumann regular ring | Regular module | 16D60 | Krull’s intersection theorem | 16E50 | 16D40 | Mathematics, general | Applications of Mathematics | Prime submodule | MATHEMATICS | Krull's intersection theorem

Journal Article

Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 8/2019, Volume 45, Issue 4, pp. 1071 - 1089

In this article, we introduce right soclean rings in which every element may be written as a sum of an element belonging to the right socle and an idempotent....

Soclean rings | Clean rings | 16E50 | Mathematics, general | Mathematics | Uniquely clean rings | 16S70 | 16U99 | Weakly soclean rings | Uniquely soclean rings | 16N60 | MATHEMATICS | ELEMENTS

Soclean rings | Clean rings | 16E50 | Mathematics, general | Mathematics | Uniquely clean rings | 16S70 | 16U99 | Weakly soclean rings | Uniquely soclean rings | 16N60 | MATHEMATICS | ELEMENTS

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2017, Volume 14, Issue 5, pp. 1 - 17

The concept of the inverse along an element was introduced by Mary in 2011. Later, Zhu et al. introduced the one-sided inverse along an element. In this paper,...

rings | 16E50 | 20M99 | Von Neumann regularity | Mathematics, general | Inverse along an element | Mathematics | semigroups | 15A09 | 16W99 | MATHEMATICS | MATHEMATICS, APPLIED | CORE INVERSE | MOORE-PENROSE | MATRICES | GENERALIZED INVERSES

rings | 16E50 | 20M99 | Von Neumann regularity | Mathematics, general | Inverse along an element | Mathematics | semigroups | 15A09 | 16W99 | MATHEMATICS | MATHEMATICS, APPLIED | CORE INVERSE | MOORE-PENROSE | MATRICES | GENERALIZED INVERSES

Journal Article

Communications in Algebra, ISSN 0092-7872, 04/2014, Volume 42, Issue 4, pp. 1619 - 1629

In this article we partially answer two open questions concerning clean rings. First, we demonstrate that if a quasi-continuous module is strongly clean then...

Primary 16E50 | Strongly clean ring | Dedekind-finite | Secondary 16D50, 16D70 | MATHEMATICS | EXCHANGE RINGS | 16D70 | Secondary 16D50 | 16U99 | Algebra

Primary 16E50 | Strongly clean ring | Dedekind-finite | Secondary 16D50, 16D70 | MATHEMATICS | EXCHANGE RINGS | 16D70 | Secondary 16D50 | 16U99 | Algebra

Journal Article

Results in Mathematics, ISSN 1422-6383, 2/2014, Volume 65, Issue 1, pp. 213 - 222

We study some generalizations of the notion of regular crossed products K * G. For the case when K is an algebraically closed field, we give necessary and...

regular ring | twisted group ring | Secondary 20C07 | 16S34 | 16E50 | Mathematics, general | Mathematics | Crossed product | Primary 16S35 | Mathematics Subject Classification : Primary 16S35, Secondary 20C07, 16S34, 16E50 | MATHEMATICS | TWISTED GROUP RINGS | MATHEMATICS, APPLIED | RADICALS | Algebra

regular ring | twisted group ring | Secondary 20C07 | 16S34 | 16E50 | Mathematics, general | Mathematics | Crossed product | Primary 16S35 | Mathematics Subject Classification : Primary 16S35, Secondary 20C07, 16S34, 16E50 | MATHEMATICS | TWISTED GROUP RINGS | MATHEMATICS, APPLIED | RADICALS | Algebra

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 2/2017, Volume 151, Issue 1, pp. 181 - 198

We present equivalent conditions of reverse order law for the (b, c)-inverse $${(a_1a_2)^{(b, c)}=a_2^{(b, s)}a_1^{(t, c)}}$$ ( a 1 a 2 ) ( b , c ) = a 2 ( b ,...

16B99 | ( b , c )-inverse | 16E50 | semigroup | Mathematics, general | generalized inverse | Mathematics | 15A09 | the inverse along an element | (b, c)-inverse | MATHEMATICS | MATRIX | OUTER GENERALIZED INVERSES | RINGS | PRODUCT | IMAGE-KERNEL (P | Q)-INVERSES

16B99 | ( b , c )-inverse | 16E50 | semigroup | Mathematics, general | generalized inverse | Mathematics | 15A09 | the inverse along an element | (b, c)-inverse | MATHEMATICS | MATRIX | OUTER GENERALIZED INVERSES | RINGS | PRODUCT | IMAGE-KERNEL (P | Q)-INVERSES

Journal Article

Vietnam Journal of Mathematics, ISSN 2305-221X, 6/2016, Volume 44, Issue 2, pp. 329 - 338

A ring R is called left G-morphic if l(a) is a principal left ideal for each a ∈ R. A ring R is called left G-regular if R is left G-morphic and left...

P-flat module | 16D50 | 16D40 | 16E50 | Mathematics, general | G-morphic ring | Mathematics | G-regular ring | P-injective module

P-flat module | 16D50 | 16D40 | 16E50 | Mathematics, general | G-morphic ring | Mathematics | G-regular ring | P-injective module

Journal Article

Journal of Algebra, ISSN 0021-8693, 03/2016, Volume 449, pp. 355 - 399

Let R be an associative unital algebra over a field k, let p be an element of R, and let R′=R〈q|pqp=p〉. We obtain normal forms for elements of R′, and for...

Normal forms in rings and modules | Universal adjunction of an inner inverse to an element of a k-algebra | Algebra | Mathematics - Rings and Algebras

Normal forms in rings and modules | Universal adjunction of an inner inverse to an element of a k-algebra | Algebra | Mathematics - Rings and Algebras

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 01/2015, Volume 63, Issue 1, pp. 185 - 200

In this paper, we examine the question of regularity of sums of special elements that appear in the study of orthogonality and invertibility.

inverse | block matrices | outer inverses | reflexive inverses | group inverse | Pierce decomposition | MATHEMATICS | MATRICES | 16E50 | 15A09 | GENERALIZED INVERSES | Algebra | Orthogonality | Regularity | Sums

inverse | block matrices | outer inverses | reflexive inverses | group inverse | Pierce decomposition | MATHEMATICS | MATRICES | 16E50 | 15A09 | GENERALIZED INVERSES | Algebra | Orthogonality | Regularity | Sums

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2014, Volume 142, Issue 10, pp. 3635 - 3648

universal sofic groups up to isomorphism. This method is also applicable to universal hyperlinear groups, giving a positive answer to a question posed by...

Ultraproducts | Mathematical sequences | Von Neumann algebra | Algebra | Mathematical theorems | Cardinality | Model theory | Natural numbers | Mathematical rings | Continuum hypothesis | Sofic groups | Hyperlinear groups | Logic for metric structures | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | sofic groups | logic for metric structures | hyperlinear groups | Mathematics - Logic

Ultraproducts | Mathematical sequences | Von Neumann algebra | Algebra | Mathematical theorems | Cardinality | Model theory | Natural numbers | Mathematical rings | Continuum hypothesis | Sofic groups | Hyperlinear groups | Logic for metric structures | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | sofic groups | logic for metric structures | hyperlinear groups | Mathematics - Logic

Journal Article

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