Results 11 to 20 of about 1,334,146 (165)

Noetherian properties in monoid rings

Journal of Pure and Applied Algebra, 2003
Let R be a commutative unitary ring and let M be a commutative monoid. The monoid ring R [ M ] is considered as an M -graded ring where the homogeneous elements of degree s are the elements of the form aX s , a ∈ R , s ∈ M .
David E. Rush
semanticscholar   +3 more sources

The isomorphism problem for monoid rings of rank 2 monoids

Journal of Pure and Applied Algebra, 1995
Let \(R\) be a commutative ring with identity, \(M\) a finitely generated submonoid of \(\mathbb{Z}^2\), and \(N\) an arbitrary monoid. The main result of this paper is that the monoids \(M\) and \(N\) are isomorphic if (and only if) their corresponding monoid rings \(R[M]\) and \(R[N]\) are isomorphic as \(R\)-algebras. This proof is accomplished by a
J. Gubeladze
semanticscholar   +2 more sources

Classifications of Several Classes of Armendariz-like Rings Relative to an Abelian Monoid and Its Applications

Mathematics
Let M be an Abelian monoid. A necessary and sufficient condition for the class ArmM of all Armendariz rings relative to M to coincide with the class Arm of all Armendariz rings is given.
Jianwei He, Yajun Ma
doaj   +3 more sources

ON ANNIHILATOR IDEALS OF SKEW MONOID RINGS* [PDF]

Glasgow Mathematical Journal, 2009
AbstractA ring R is called a left APP-ring if the left annihilator lR(Ra) is pure as a left ideal of R for every a ∈ R; R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. Let R be a ring and M an ordered monoid.
Zhong-kui Liu, Xiaoyan Yang
semanticscholar   +2 more sources

On nil-McCoy rings relative to a monoid

Cogent Mathematics & Statistics, 2018
The concept of nil-M-McCoy (nil-McCoy ring relative to monoid M), which are generalizations of McCoy ring and nil-M-Armendariz rings have been introduced, and we investigate their properties.
Mohammad Javad Nikmehr, Vahid Aghapouramin   +1 more
exaly   +2 more sources

Multiplicity and Hilbert-Kunz Multiplicity of Monoid Rings

Tokyo Journal of Mathematics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kazufumi Eto
semanticscholar   +4 more sources

On monoid graded semihereditary rings

Communications in Algebra
In order to study graded left hereditary and left semihereditary rings graded by a cancelation monoid in terms of their modules, we need to revisit graded free, projective, injective, and flat modules and provide graded versions of specific results ...
Haneen Falah Ghalib Al-Kharsan, P. Sahandi, N. Shirmohammadi   +2 more
semanticscholar   +3 more sources

Endo-Noetherian Skew Generalized Power Series Rings [PDF]

Assiut University Journal of Multidisciplinary Scientific Research, 2023
Endo-Noetherian modules were introduced by A. Kaidi and E. Sanchez] as a generalization of Noetherian modules. A left Ɍ-module M which satisfies the ascending chain condition for endomorphic kernels is said to be endo-Noetherian.
Ramy Abdel-Khaleq, Refaat Salem, Neamat Mohamed   +2 more
doaj   +1 more source

The Reflexive Condition on Skew Monoid Rings

European Journal of Pure and Applied Mathematics, 2023
This paper is devoted to introducing and studying two concepts, σ-skew strongly M-reflexive and σ-skew strongly M-nil-reflexive on monoid rings, which are generalizations of strongly M-reflexive and M-compatible.
Eltiyeb Ali
semanticscholar   +1 more source

The Ring Homomorphisms of Matrix Rings over Skew Generalized Power Series Rings

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2021
Let  M_n (R_1 [[S_1,≤_1,ω_1]]) and M_n (R_2 [[S_2,≤_2,ω_2]]) be a matrix rings over skew generalized power series rings, where R_1,R_2 are commutative rings with an identity element, (S_1,≤_1 ),(S_2,≤_2 ) are strictly ordered monoids, ω_1:S_1→End(R_1 ),〖
Ahmad Faisol, Fitriani Fitriani
doaj   +1 more source