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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
Journal Article
Communications in Algebra, ISSN 0092-7872, 08/2014, Volume 42, Issue 8, pp. 3507 - 3540
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
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
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)
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
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
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)
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
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
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 05/2015, Volume 146, Issue 1, pp. 1 - 21
Le Riche, Meldrum and Van der Walt introduced the concept of a group near-ring. Thereafter, starting with an ideal in the base near-ring, they constructed two... 
16D25 | prime | MATHEMATICS | ideal | near-ring | module | monogenic
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
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
Journal Article
by Shen, L
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
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)
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
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)
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
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
Journal Article
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