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2016, London Mathematical Society lecture note series, ISBN 1316619583, Volume 435., vii, 235 pages
This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has... 
Grothendieck groups | Graded rings | Rings (Algebra)
Book
2013, Mathematical surveys and monographs, ISBN 9780821898468, Volume 189, xiii, 336
Book
Journal of Algebra, ISSN 0021-8693, 10/2019, Volume 536, pp. 82 - 101
Given a Z-graded ring A and a subring R⊆A, it is natural to ask whether A can be realised as the Cuntz–Pimsner ring of some R-system. In this paper, we derive... 
Groupoid algebras | Steinberg algebras | Graded rings | Cuntz-Pimsner rings | MATHEMATICS | ALGEBRAS | IDEAL STRUCTURE
Journal Article
2002, Series in algebra, ISBN 9789810247454, Volume 9., xi, 205
Book
Journal of Algebra, ISSN 0021-8693, 11/2019, Volume 538, pp. 207 - 231
Let C be a commutative noetherian domain, G be a finitely generated abelian group which acts on C and B=C#G be the skew group ring. For a prime ideal I◁C, we... 
Idealizer ring | Noetherian graded ring | Idealiser ring | Skew Group ring | MATHEMATICS
Journal Article
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, ISSN 0253-4142, 04/2019, Volume 129, Issue 2, p. 1
Let R be a ring graded by an arbitrary set A. We show that R decomposes as the sum of the well-described graded ideals plus (maybe) a certain subgroup. We also... 
Graded ring | structure theory | MATHEMATICS | GRADINGS
Journal Article
Communications in Algebra, ISSN 0092-7872, 09/2018, Volume 46, Issue 9, pp. 4079 - 4089
In this paper we introduce and study the notion of a graded (strongly) nil clean ring which is group graded. We also deal with extensions of graded (strongly)... 
matrix rings | 16W50 | 16S34 | nil clean rings | 16S50 | group rings | Graded rings and modules | 16U99 | MATHEMATICS | Rings (mathematics) | Mathematics - Rings and Algebras
Journal Article
International Journal of Mechanical Sciences, ISSN 0020-7403, 08/2014, Volume 85, pp. 187 - 195
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 4/2018, Volume 154, Issue 2, pp. 343 - 361
A D-structure on a ring A with identity is a family of self-mappings indexed by the elements of a monoid G and subject to a long list of rather natural... 
16S20 | 16W50 | normalizing extension | subnormalizing extension | Mathematics, general | Mathematics | skew polynomial ring | skew monoid ring | graded ring | 16A05 | 16S36 | MATHEMATICS | Computer science | Algebra
Journal Article
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 02/2019, Volume 292, Issue 2, pp. 389 - 401
Given a morphism F:X→Y from a Mori Dream Space X to a smooth Mori Dream Space Y and quasicoherent sheaves F on X and G on Y, we describe the inverse image of G... 
Primary: 14C20; Secondary: 14A10 | Cox ring | direct image | inverse image | graded module | quasicoherent sheaf | 14L30 | MATHEMATICS
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 10/2016, Volume 15, Issue 8
We investigate the graded Brown-McCoy and the classical Brown-McCoy radical of a graded ring, which is the direct sum of a family of its additive subgroups... 
Graded rings and modules | modular ideals | Brown-McCoy radical | MATHEMATICS | MATHEMATICS, APPLIED | JACOBSON | Mathematics - Rings and Algebras
Journal Article
2012, ISBN 9814365130, x, 284
Book
Mathematische Zeitschrift, ISSN 0025-5874, 12/2018, Volume 290, Issue 3, pp. 1249 - 1276
We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free d-generator Lie rings $$\mathfrak {f}_{c,d}$$ fc,d of... 
Graded ideal zeta functions | Local functional equations | Free nilpotent Lie rings | 11M41 | 11S40 | Mathematics, general | 17B70 | Mathematics | MATHEMATICS | ALGEBRAS | ZETA-FUNCTIONS | SUBGROUPS
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 12/2017, Volume 20, Issue 6, pp. 1483 - 1494
In this article we introduce the notion of a controlled group graded ring. Let G be a group, with identity element e, and let R = ⊕ g∈G R g be a unital... 
16W50 | Non-associative Rings and Algebras | Strongly graded ring | Commutative Rings and Algebras | Mathematics | Skew group ring | Associative Rings and Algebras | Graded ring | Bimodule | 16D40 | Crossed product | 16S35 | Picard group | MATHEMATICS | Algebra | Naturvetenskap | Algebra and Logic | Algebra och logik | Natural Sciences | Matematik
Journal Article
Journal of Algebra, ISSN 0021-8693, 11/2012, Volume 369, pp. 351 - 359
Cox rings of normal prevarieties are factorially graded, i.e. homogeneous elements allow a unique decomposition into homogeneous factors. We study this... 
Commutative algebra | Graded rings | Cox rings | Unique factorization | Algebraic geometry | MATHEMATICS | Algebra
Journal Article
Communications in Algebra, ISSN 0092-7872, 03/2019, Volume 47, Issue 3, pp. 1114 - 1124
Our approach to structural matrix rings defines them over preordered directed graphs. A grading of a structural matrix ring is called a good grading if its... 
16W50 (Primary) | Graded algebra | 16S50 (Secondary) | directed graph | MATHEMATICS | ALGEBRAS | GRAPHS | Graphs | Graph theory | Grading | 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
Journal of Algebra and its Applications, ISSN 0219-4988, 06/2018, Volume 17, Issue 6
Journal Article
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