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Taiwanese Journal of Mathematics, ISSN 1027-5487, 2016, Volume 20, Issue 6, pp. 1231 - 1250
Let R be an associative ring with identity, S a multiplicative subset of R, and M a right R-module. Then M is called an S-Noetherian module if for each... 
Ore extension | S-Noetherian module | Right S-Noetherian ring | Hilbert basis theorem | MATHEMATICS
Journal Article
Communications in Algebra, ISSN 0092-7872, 02/2018, Volume 46, Issue 2, pp. 863 - 869
In this paper we study right S-Noetherian rings and modules, extending notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative... 
Completely prime right ideals | right S-Noetherian rings | Oka families of right ideals | point annihilator sets | MATHEMATICS | PRIME IDEAL PRINCIPLE | Modules | Rings (mathematics)
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2011, Volume 363, Issue 1, pp. 457 - 500
Let B = B(X,L,σ) be the twisted homogeneous coordinate ring of a projective variety X over an algebraically closed field k. We construct and investigate a... 
Geometry | Algebra | Mathematical theorems | Property rights | Functors | Coordinate systems | Mathematical rings | Automorphisms | Subrings | MATHEMATICS | ALGEBRAS | KLEIMAN-BERTINI THEOREM | NONCOMMUTATIVE PROJECTIVE GEOMETRY | AMPLENESS | DUALIZING COMPLEXES | SURFACES | SCHEMES
Journal Article
Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 03/2017, Volume 54, Issue 1, pp. 82 - 96
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2018, Volume 13, Issue 2, pp. 443 - 460
Let $${\mathcal {A}}$$ A be an abelian category. In this paper we study monoform objects and atoms introduced by Kanda. We classify full subcategories of... 
Serre subcategory | 18E10 | Algebra | Abelian category | Right noetherian rings | Functional Analysis | Algebraic Topology | Mathematics | Number Theory | Grothendieck category | 18E15 | MATHEMATICS | MODULES | NOETHERIAN-RINGS | CLASSIFYING SUBCATEGORIES | CLASSIFICATION
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2007, Volume 359, Issue 4, pp. 1499 - 1515
Journal Article
Bulletin of Mathematical Sciences, ISSN 1664-3607, 4/2015, Volume 5, Issue 1, pp. 121 - 136
Dimensions like Gelfand, Krull, Goldie have an intrinsic role in the study of theory of rings and modules. They provide useful technical tools for studying... 
Couniserial dimension | 16P70 | 13E10 | Uniform module | Indecomposable decomposition | Mathematics | Semisimple module | Von Neumann regular ring | Maximal right quotient ring | Uniserial dimension | Primary 16D70 | Mathematics, general | 16D90 | Secondary 03E10 | MATHEMATICS | MODULES | RINGS | DOMAINS
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 4/2019, Volume 45, Issue 2, pp. 429 - 445
In this paper, we study retractable modules and coretractable modules over a formal triangular matrix ring $$T=\left[ \begin{array}{rr} A &{} 0 \\ M &{} B \\... 
Right Kasch rings | 16D70 | 16S50 | Mathematics, general | Secondary 16D20 | Mathematics | Coretractable modules | Formal triangular matrix rings | 16D80 | Primary 16D10 | Retractable modules | MATHEMATICS
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 8/2018, Volume 13, Issue 4, pp. 833 - 847
A ring is said to be right (resp., left) regular-duo if every right (resp., left) regular element is regular. The structure of one-sided regular elements is... 
16U20 | 16U80 | right (left) regular element | right (left) regular-duo ring | Mathematics, general | Mathematics | upper triangular matrix ring | right (left) Ore domain | MATHEMATICS | ARMENDARIZ RINGS | Mathematical analysis | Rings (mathematics)
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2009, Volume 137, Issue 7, pp. 2265 - 2271
We prove that for a ring R, the following are equivalent: (i) Every right R-module is a direct sum of extending modules, and (ii) R has finite type and right... 
Ring theory | Serial rings | Mathematical rings | Algebra | Mathematical theorems | Property rights | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2009, Volume 137, Issue 9, pp. 2899 - 2903
Let R be a prime ring in which the nilpotent elements commute. If R has finite right uniform dimension or its maximal right quotient ring is Dedekind finite,... 
Mathematical theorems | Algebra | Mathematical sets | Quotients | Mathematical rings | Commuting | Subrings | Prime ring | Nilpotent element | Maximal right quotient ring | MATHEMATICS | MATHEMATICS, APPLIED | maximal right quotient ring | INVARIANT ADDITIVE SUBGROUPS | nilpotent element
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 8/2015, Volume 18, Issue 4, pp. 1123 - 1134
In this paper we study right Mori Orders, which are those prime Goldie rings that satisfy the ascending chain condition on integral right ν-ideals. We examine... 
Secondary 13E99 | Associative Rings and Algebras | Non-associative Rings and Algebras | Primary 13F05 | Commutative Rings and Algebras | Mori properties | Mathematics | Right divisorial ideals
Journal Article
Communications in Algebra, ISSN 0092-7872, 07/2019, Volume 47, Issue 7, pp. 2843 - 2854
In this paper, we study rings with only finitely many essential right ideals (right fe-rings for short). We see that these rings have some similar properties... 
finiteness conditions | Essential right ideal | fe-ring | MATHEMATICS
Journal Article
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, ISSN 1370-1444, 04/2014, Volume 21, Issue 2, pp. 303 - 318
Let R be an arbitrary ring with identity and M a right R-module with S = End(R) (M). In this paper we introduce pi-Rickart modules as a generalization of... 
MATHEMATICS | Fitting module | Rickart module | generalized right principally projective ring | pi-Rickart module | RINGS | Analysis | Rings (Algebra) | 16D40 | 13C99 | 16D80
Journal Article
Algebra Colloquium, ISSN 1005-3867, 03/2015, Volume 22, Issue 1, pp. 119 - 130
We investigate the structure of rings over which every finitely generated (delta-supplemented module is supplemented. Some characterizations of this type of... 
right δ-ring | (δ)local module | (δ)small submodule | (δ-)supplemented module | MATHEMATICS | right Delta-ring | MATHEMATICS, APPLIED | (delta-)small submodule | circle plus-(delta-)supplemented module | RINGS | (delta-)local module | SEMIPERFECT | (delta-)supplemented module
Journal Article
Mathematical Notes, ISSN 0001-4346, 5/2015, Volume 97, Issue 5, pp. 937 - 940
It is proved that a variety of associative rings is left and right locally Noetherian if and only if every finitely generated ring in the variety contains only... 
idempotent | Mathematics, general | Mathematics | variety of associative rings | left (right) locally Noetherian ring | MATHEMATICS
Journal Article
Communications in Algebra, ISSN 0092-7872, 01/2001, Volume 29, Issue 2, pp. 639 - 660
We say a ring with unity is right principally quasi-Baer (or simply, right p.q.-Baer) if the right annihilator of a principal right ideal is generated (as a... 
Quasi-Baer rings | Baer rings | Annihilators | Right PP rings | Biregular rings | Semicentral idempotents | semicentral idempotents | MATHEMATICS | MODULES | quasi-Baer rings | FPF RINGS | right PP rings | biregular rings | annihilators
Journal Article
Communications in Algebra, ISSN 0092-7872, 04/2015, Volume 43, Issue 4, pp. 1687 - 1697
This note is concerned with generalizations of commutativity. We introduce identity-symmetric and right near-commutative, and study basic structures of rings... 
Generalization of commutativity | Skew-trivial extension | Right duo ring | Identity-symmetric ring | Right near-commutative ring | MATHEMATICS | DUO RINGS
Journal Article
Communications in Algebra, ISSN 0092-7872, 01/2014, Volume 42, Issue 1, pp. 81 - 95
Let A 1 : =  [t, ∂] be the first algebra over a field of characteristic zero. Let Aut (A 1 ) be the automorphism group of the ring A 1 . One can associate to... 
Right ideals | First Weyl agebra | Automorphism group | MATHEMATICS | 16S32 | 16W20 | Isomorphism | Algebra | Automorphisms | Subgroups | Rings (mathematics)
Journal Article
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