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MathematicsLet 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
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Fractional skew monoid rings [PDF]
Journal of Algebra, 2004 Given an action of a monoid $T$ on a ring $A$ by ring endomorphisms, and an Ore subset $S$ of $T$, a general construction of a fractional skew monoid ring $S^{\rm op} * A * T$ is given, extending the usual constructions of skew group rings and of skew semigroup rings.
Enrique Pardo +2 more
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PRIME RADICALS IN UP-MONOID RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2012 A monoid \(G\) is a `unique product monoid' (up-monoid) if for any two nonempty finite subsets \(A\) and \(B\) of \(G\), there is at least one \(c\in G\) which has a unique representation as \(c=ab\) with \(a\in A\) and \(b\in B\). Here the authors study the relationships between nil-related properties of a ring and those of the monoid ring \(RG ...
Cheon, Jeoung Soo, Kim, Jin-A
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Nil-Armendariz Rings Relative to a Monoid
Mediterranean Journal of Mathematics, 2012 The notion of an Armendariz ring has been generalized in many different ways. Here another generalization is presented. For a monoid \(M\), \(R[M]\) is the monoid ring over \(R\) and \(\text{nil}(R)\) is the set of nilpotent elements of \(R\). A ring \(R\) is called `nil-Armendariz relative to \(M\)' if whenever \(\alpha=\sum_{i=1}^na_ig_i,\beta=\sum_ ...
Ebrahim Hashemi
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Galois orders in skew monoid rings
Journal of Algebra, 2010 The paper deals with ring extensions \(\Gamma\subset U\) of an integral domain \(\Gamma\), in particular, a general class of subrings of invariants in twisted Galois semigroup rings which the authors call Galois orders. The study of such Galois orders is inspired by the authors' previous work on Harish-Chandra categories [Fibers of characters in Harish-
Vyacheslav Futorny
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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 +2 more
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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
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SOLVING DIFFERENCE EQUATIONS IN SEQUENCES: UNIVERSALITY AND UNDECIDABILITY
Forum of Mathematics, Sigma, 2020 We study solutions of difference equations in the rings of sequences and, more generally, solutions of equations with a monoid action in the ring of sequences indexed by the monoid. This framework includes, for example, difference equations on grids (for
GLEB POGUDIN +2 more
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On the Monoid of Unital Endomorphisms of a Boolean Ring [PDF]
Axioms, 2021 Let X be a nonempty set and P(X) the power set of X. The aim of this paper is to provide an explicit description of the monoid End1P(X)(P(X)) of unital ring endomorphisms of the Boolean ring P(X) and the automorphism group Aut(P(X)) when X is finite. Among other facts, it is shown that if X has cardinality n≥1, then End1P(X)(P(X))≅Tnop, where Tn is the
Bana Al Subaiei, Noômen Jarboui
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On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings
International Journal of Analysis and Applications, 2023 In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer ...
Eltiyeb Ali
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