Results 91 to 100 of about 677,523 (211)
A commutative version of the group ring
We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings.
Mannan, W.H.
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Polynomial Rings over Pseudovaluation Rings
International Journal of Mathematics and Mathematical Sciences, 2007 Let R be a ring. Let σ be an automorphism of R. We define a σ-divided ring and prove the following. (1) Let R be a commutative pseudovaluation ring such that x∉P for any P∈Spec(R[x,σ]) . Then R[x,σ] is also a pseudovaluation ring.
V. K. Bhat
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Embedding Noetherian Rings in Artinian Rings
Journal of Algebra, 2001 A well-known theorem of \textit{A. H. Schofield} [``Representation of rings over skew fields'', Lond. Math. Soc. Lect. Note Ser. 92, CUP, Cambridge (1985; Zbl 0571.16001)] asserts that an algebra \(A\) over a field can be embedded in a right Artinian ring if and only if there is a faithful Sylvester rank function on finitely presented \(A\)-modules. By
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Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum. [PDF]
Math Ann, 2023 Bik A, Danelon A, Draisma J.
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Flat local morphisms of rings with prescribed depth and dimension
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 For any pairs of integers (n,m) and (d, e) such that 0 ≤ n ≤ m, 0 ≤ d _ e, d ≤ n, e ≤ m and n -d ≤ m - e we construct a local flat ring morphism of noetherian local rings u : A → B such that dim(A) = n; depth(A) = d; dim(B) = m and depth(B) = e.
Ionescu Cristodor
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The Injective Spectrum of a Right Noetherian Ring [PDF]
, 2019 The injective spectrum is a topological space associated to a ring R, which agrees with the Zariski spectrum when R is commutative noetherian. We consider injective spectra of right noetherian rings (and locally noetherian Grothendieck categories) and ...
Gulliver, Harry
core
, 2002 Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
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On the structure of some minimax-antifinitary modules
Karpatsʹkì Matematičnì Publìkacìï, 2015 Let $R$ be a ring and $G$ a group. An $R$-module $A$ is said to be {\it minimax} if $A$ includes a noetherian submodule $B$ such that $A/B$ is artinian.
V.A. Chupordia
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On flat extensions of Noetherian rings [PDF]
Proceedings of the American Mathematical Society, 1965 In this note a ring will always mean a commutative, Noetherian ring with a unit. Let (B, p) be a flat extension of the ring A (i.e. B a ring and p a ring-homomorphism of A in B such that B regarded as A-module is flat), M a finitely generated A-module and N a submodule of M.
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Subrings of I-rings and S-rings
International Journal of Mathematics and Mathematical Sciences, 1997 Let R be a non-commutative associative ring with unity 1≠0, a left R-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M.
Mamadou Sanghare
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