Results 61 to 70 of about 146 (134)
On hereditary rings and NoetherianV-rings [PDF]
Pacific Journal of Mathematics, 1982 The purpose of this paper is to examine conditions under which (1) a left noetherian left F-ring is left hereditary and (2) a left noetherian left F-ring is a two sided noetherian F-ring. For (1), left noetherian left F-rings which satisfy the restricted left minimum (RLM) condition are examined.
openaire +3 more sources
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
Bi-artinian noetherian rings [PDF]
Glasgow Mathematical Journal, 2001 A noetherian ring R satisfies the descending chain condition on two-sided ideals (“is bi-artinian”) if and only if, for each prime P ∈ spec(R), R/P has a unique minimal ideal (necessarily idempotent and left-right essential in R/P). The analogous statement for merely right noetherian rings is false, although our proof does not use the full ...
openaire +2 more sources
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
Noetherian rings of composite generalized power series
Open MathematicsLet A⊆BA\subseteq B be an extension of commutative rings with identity, (S,≤)\left(S,\le ) a nonzero strictly ordered monoid, and S*=S\{0}{S}^{* }\left=S\backslash \left\{0\right\}.
Oh Dong Yeol
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
Neutrosophic Ideals in Artinian Rings and Their Application to AI‐Driven Uncertainty Classification
Journal of Mathematics, Volume 2026, Issue 1, 2026.This work examines the behaviour of neutrosophic ideals within the framework of Artinian rings. A key finding shows that a ring with unity is left (or right) Artinian if and only if every neutrosophic left (or right) ideal takes only finitely many possible values.
Amr Elrawy +4 more
wiley +1 more source
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
doaj +1 more source
On the global dimension of Noetherian bi-amalgamated algebras along ideals
Journal of Taibah University for Science, 2017 Let f : A → B and g : A → C be two ring homomorphisms and let J and J′ be two ideals of B and C, respectively, such that f−1(J) = g−1(J′). The bi-amalgamation of A with (B, C) along (J, J′) with respect to (f, g) is the subring of B × C given by A⋈f,g(J ...
Mohammed Tamekkante, Khalid Louartiti
doaj +1 more source
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