Communications in Algebra, ISSN 0092-7872, 10/2018, Volume 46, Issue 10, pp. 4174 - 4175

In this corrigendum, we correct the statement and proof of Lemma 3.2, revise the proofs of Lemma 3.3 and Theorem 3.5, retract Proposition 3.10 and correct...

SA-ring | Primary 16D25 | 16D70 | 54G05

SA-ring | Primary 16D25 | 16D70 | 54G05

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2014, Volume 42, Issue 8, pp. 3507 - 3540

We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane...

Irreducible components | (noncommutative complete intersections) NCCI | Primary 16G30, 16G60, 16D25 | Secondary 16A24 | Representation spaces | (representational complete intersections) RCI | Golod-Shafarevich complex | HILBERT SERIES | VARIETIES | AUTOMORPHISMS | Primary 16G30 | 16D25 | 16G60 | MATHEMATICS | MATRICES | WEYL ALGEBRA | Algebra | Representations | Planes | Intersections | Modules

Irreducible components | (noncommutative complete intersections) NCCI | Primary 16G30, 16G60, 16D25 | Secondary 16A24 | Representation spaces | (representational complete intersections) RCI | Golod-Shafarevich complex | HILBERT SERIES | VARIETIES | AUTOMORPHISMS | Primary 16G30 | 16D25 | 16G60 | MATHEMATICS | MATRICES | WEYL ALGEBRA | Algebra | Representations | Planes | Intersections | Modules

Journal Article

Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2015, Volume 45, Issue 4, pp. 1177 - 1195

This paper determines the structure of an associative ring R when either all of its additive subgroups, all of its subrings, all of its (right) ideals, or all...

MATHEMATICS | 16P70 | 16D70 | 16W10 | 16D25

MATHEMATICS | 16P70 | 16D70 | 16W10 | 16D25

Journal Article

Communications in Algebra, ISSN 0092-7872, 11/2019, Volume 47, Issue 11, pp. 4740 - 4742

It is well-known that the Jacobson radical of a unital ring R is the largest superfluous right ideal of R. While a simple example shows this to be false for...

Jacobson radical | 16D80 | Primary 16N20 | non-unital ring | Secondary 16D25 | superfluous ideal | MATHEMATICS | Mathematics - Rings and Algebras

Jacobson radical | 16D80 | Primary 16N20 | non-unital ring | Secondary 16D25 | superfluous ideal | MATHEMATICS | Mathematics - Rings and Algebras

Journal Article

Communications in Algebra, ISSN 0092-7872, 02/2019, Volume 47, Issue 2, pp. 836 - 851

In this article, we first observe a sort of property of ideals generated by zero-dividing polynomials over reversible rings, in relation with products of...

(right) partially reflexive ring | reversible ring | reflexive ring | Matrix ring | 16S36 | polynomial ring | 16D25 | MATHEMATICS | ARMENDARIZ RINGS | Polynomials | Rings (mathematics)

(right) partially reflexive ring | reversible ring | reflexive ring | Matrix ring | 16S36 | polynomial ring | 16D25 | MATHEMATICS | ARMENDARIZ RINGS | Polynomials | Rings (mathematics)

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...

Mathematics - Rings and Algebras

Mathematics - Rings and Algebras

Journal Article

Communications in Algebra, ISSN 0092-7872, 12/2018, Volume 46, Issue 12, pp. 5234 - 5240

In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We...

perfect localization | Hereditary torsion theory | 16D70 | left hereditary ring | 16D50 | left V-ring | 16D90 | left QI-ring | 16D25 | MATHEMATICS | RINGS

perfect localization | Hereditary torsion theory | 16D70 | left hereditary ring | 16D50 | left V-ring | 16D90 | left QI-ring | 16D25 | MATHEMATICS | RINGS

Journal Article

Communications in Algebra, ISSN 0092-7872, 11/2016, Volume 44, Issue 11, pp. 4585 - 4608

Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime...

16D20 | Prime ideal principle | Primary: 16D25 | Maximal implies prime | Oka family of ideals | 16N60 | Secondary: 13A15 | MATHEMATICS | NOETHERIAN ALGEBRAS | FIELDS | RINGS | Polynomials | Algebra | Rings (mathematics)

16D20 | Prime ideal principle | Primary: 16D25 | Maximal implies prime | Oka family of ideals | 16N60 | Secondary: 13A15 | MATHEMATICS | NOETHERIAN ALGEBRAS | FIELDS | RINGS | Polynomials | Algebra | Rings (mathematics)

Journal Article

Communications in Algebra, ISSN 0092-7872, 09/2017, Volume 45, Issue 9, pp. 3886 - 3891

In this paper, we study the graded Thierrin radical and the classical Thierrin radical of a graded ring, which is the direct sum of a family of its additive...

16W50 | maximal modular one-sided ideal | Graded rings and modules | 16N80 | 16D25 | Thierrin radical | MATHEMATICS | Subgroups | Additives | Algebra | Radicals

16W50 | maximal modular one-sided ideal | Graded rings and modules | 16N80 | 16D25 | Thierrin radical | MATHEMATICS | Subgroups | Additives | Algebra | Radicals

Journal Article

Communications in Algebra, ISSN 0092-7872, 10/2019, Volume 47, Issue 10, pp. 4194 - 4209

Tauvel's height formula, which provides a link between the height of a prime ideal and the Gelfand-Kirillov dimension of the corresponding factor algebra, is...

20G42 | Primary 16T20 | CGL extension | Height formula | 16S36 | quantum nilpotent algebra | Secondary 16D25 | 16P90 | Gelfand-Kirillov dimension | MATHEMATICS | PRIME | ORE EXTENSIONS | CATENARITY | DIMENSION | SPECTRA | IDEALS | Algebra

20G42 | Primary 16T20 | CGL extension | Height formula | 16S36 | quantum nilpotent algebra | Secondary 16D25 | 16P90 | Gelfand-Kirillov dimension | MATHEMATICS | PRIME | ORE EXTENSIONS | CATENARITY | DIMENSION | SPECTRA | IDEALS | Algebra

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 05/2015, Volume 146, Issue 1, pp. 1 - 21

Journal Article

Acta Universitatis Sapientiae, Mathematica, ISSN 2066-7752, 08/2019, Volume 11, Issue 1, pp. 224 - 233

Abstract Let M be an R-module and I be an ideal of R. We say that M is I-Rad-⊕-supplemented, provided for every submodule N of M, there exists a direct summand...

Rad(-⊕-)supplemented module | 16D10 | I-Rad-⊕-supplemented module | supplement | 16D50 | 16D25

Rad(-⊕-)supplemented module | 16D10 | I-Rad-⊕-supplemented module | supplement | 16D50 | 16D25

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 8/2017, Volume 152, Issue 2, pp. 269 - 290

The present paper is devoted to the study of some subclasses of H-rings, i.e., rings in which all subrings are ideals. In the description of H-rings an...

ideal | 13B02 | Mathematics, general | H-ring | Mathematics | 13C05 | 16D25 | IDENTITY | MATHEMATICS | FILIAL RINGS

ideal | 13B02 | Mathematics, general | H-ring | Mathematics | 13C05 | 16D25 | IDENTITY | MATHEMATICS | FILIAL RINGS

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 10/2018, Volume 156, Issue 1, pp. 38 - 46

A ring R is called left (Kasch) dual if every (maximal) left ideal of R is a left annihilator. R is left CF if every left ideal of R is the left annihilator of...

CF ring | dual ring | 16S34 | perfect duality | Mathematics, general | group ring | Mathematics | Kasch ring | 16D25 | MATHEMATICS

CF ring | dual ring | 16S34 | perfect duality | Mathematics, general | group ring | Mathematics | Kasch ring | 16D25 | MATHEMATICS

Journal Article

01/2017

Journal of Algebra and Its Applications (2020) From Morita theoretic viewpoint, computing Morita invariants is important. We prove that the intersection of the...

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2016, Volume 44, Issue 5, pp. 2067 - 2074

Rings in which all accessible subrings are ideals (i.e., rings in which the relation of being an ideal is transitive) are called filial. This article concerns...

Primary: 16D25 | Ideal | Secondary: 13B02 | Filial ring | Theorems | Algebra | Conferences | Accessibility | Imbeddings | Radicals | Rings (mathematics)

Primary: 16D25 | Ideal | Secondary: 13B02 | Filial ring | Theorems | Algebra | Conferences | Accessibility | Imbeddings | Radicals | Rings (mathematics)

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2018, Volume 46, Issue 8, pp. 3605 - 3607

Let A be a finite dimensional associative algebra over a perfect field and let R be the radical of A. We show that for every one-sided ideal I of A there...

16D20 | Wedderburn-Malcev decomposition | one-sided ideals | Finite dimensional algebra | 16P10 | 16D25 | Wedderburn–Malcev decomposition | MATHEMATICS | Mathematics - Rings and Algebras

16D20 | Wedderburn-Malcev decomposition | one-sided ideals | Finite dimensional algebra | 16P10 | 16D25 | Wedderburn–Malcev decomposition | MATHEMATICS | Mathematics - Rings and Algebras

Journal Article

Communications in Algebra, ISSN 0092-7872, 03/2019, Volume 47, Issue 3, pp. 1348 - 1375

We define a ring R to be right -Baer if the right annihilator of a cyclic projective right R-module in R is generated by an idempotent. This class of rings...

16W60 | 16S50 | 16S85 | I-prime | Annihilator | generalized upper triangular matrix ring | 16D25 | 16N60 | 16D70 | 16D40 | formal power series ring | 16S36 | cyclic projective Baer ring | MATHEMATICS | BAER | MODULES | RINGS | Polynomials | Equivalence | Power series | Modules | Rings (mathematics)

16W60 | 16S50 | 16S85 | I-prime | Annihilator | generalized upper triangular matrix ring | 16D25 | 16N60 | 16D70 | 16D40 | formal power series ring | 16S36 | cyclic projective Baer ring | MATHEMATICS | BAER | MODULES | RINGS | Polynomials | Equivalence | Power series | Modules | Rings (mathematics)

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2012, Volume 40, Issue 5, pp. 1690 - 1703

Filial rings are rings in which the relation of being an ideal is transitive. We continue the study of commutative filial rings started in [2, 3]. In...

Noetherian ring | 16D70 | Ideal | 16D25 | Filial ring | MATHEMATICS | ALGEBRAS

Noetherian ring | 16D70 | Ideal | 16D25 | Filial ring | MATHEMATICS | ALGEBRAS

Journal Article

Formalized Mathematics, ISSN 1426-2630, 12/2018, Volume 26, Issue 4, pp. 277 - 283

We formalize in the Mizar system [3], [4] basic definitions of commutative ring theory such as prime spectrum, nilradical, Jacobson radical, local ring, and...

68T99 | semi-local ring | nilradical | 14A05 | local ring | Jacobson radical | prime spectrum | Zariski topology | 03B35 | 16D25

68T99 | semi-local ring | nilradical | 14A05 | local ring | Jacobson radical | prime spectrum | Zariski topology | 03B35 | 16D25

Journal Article

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