Results 91 to 100 of about 2,667 (226)
Module structure of Weyl algebras
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The seminal paper (Stafford, J. Lond. Math. Soc. (2) 18 (1978), no. 3, 429–442) was a major step forward in our understanding of Weyl algebras. Beginning with Serre's Theorem on free summands of projective modules and Bass' Stable Range Theorem in commutative algebra, we attempt to trace the origins of this work and explain how it led to ...
Gwyn Bellamy
wiley +1 more source
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
An Approach to Baer Criteria of Injectivity Versus Ideal Injectivity
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.This paper aims to investigate the Baer‐type criteria for the injectivity of S‐acts. Unlike modules over rings, where the Baer criterion for injectivity is valid, this criterion remains an open problem for acts over semigroups. Every injective S‐act is ideal injective, but the converse does not hold in general.
Hasan Barzegar, Anwar Saleh Alwardi
wiley +1 more source
Cartan-Eilenberg 复形的Foxby 等价(Foxby equivalences of Cartan-Eilenberg complexes)
Zhejiang Daxue xuebao. Lixue ban, 2019 Let R be a commutative noetherian ring with a semi-dualizing module C. We introduce CE (abbreviation for Cartan-Eilenberg) Auslander class CΕ - 𝓐C( R ) and CE Bass class CΕ - 𝓑C ( R ) ,and extend the Foxby equivalence to the setting of CE complexes.
ZHANGChunxia(张春霞) +1 more
doaj +1 more source
b‐Filter Grade of an Ideal a for Triangulated Categories
Journal of Mathematics, Volume 2026, Issue 1, 2026.Let a and b be two homogeneous ideals in a graded‐commutative Noetherian ring R, and let X be an object in a compactly generated R‐linear triangulated category T. We introduce the notion of the b‐filter grade of a on X, denoted by f‐gradb,a,X, and provide several characterizations and bounds for this invariant. In addition, we explore the relationships
Li Wang +4 more
wiley +1 more source
Nontriviality of rings of integral‐valued polynomials
Mathematische Nachrichten, Volume 298, Issue 12, Page 3974-3994, December 2025.Abstract Let S$S$ be a subset of Z¯$\overline{\mathbb {Z}}$, the ring of all algebraic integers. A polynomial f∈Q[X]$f \in \mathbb {Q}[X]$ is said to be integral‐valued on S$S$ if f(s)∈Z¯$f(s) \in \overline{\mathbb {Z}}$ for all s∈S$s \in S$. The set IntQ(S,Z¯)${\mathrm{Int}}_{\mathbb{Q}}(S,\bar{\mathbb{Z}})$ of all integral‐valued polynomials on S$S ...
Giulio Peruginelli, Nicholas J. Werner
wiley +1 more source
A commutative version of the group ring [PDF]
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.
core
The Laskerian property, power series rings and Noetherian spectra [PDF]
, 1980 We show that if the power series ring R [ [ X ] ] R[[X]] in one indeterminate over a commutative ring R with identity is Laskerian, then R is Noetherian. On the other hand, if R
William Heinzer, Robert Gilmer
core +1 more source
FINITENESS PROPERTIES OF FORMAL LOCAL HOMOLOGY MODULES [PDF]
Romanian Journal of Mathematics and Computer Science, 2015 Let (R, m) be a commutative Noetherian ring, a an ideal of R and M an Artinian R-module. In this paper, we investigate the structure of the formal local homology. We prove several results concerning finiteness properties of formal local homology module.
M. H. BIJAN-ZADEH,, S. GHADERI
doaj
When Is a Simple Ring Noetherian?
Journal of Algebra, 1996 A module is called a \(CS\)-module if every submodule is essential in a direct summand. It is proved that a simple ring \(R\) is right Noetherian provided every cyclic singular right \(R\)-module is \(CS\). In addition, a simple ring \(R\) is right hereditary right Noetherian provided every proper cyclic right \(R\)-module is quasi-injective.
Van Huynh, Dinh +2 more
openaire +1 more source