منابع مشابه
On quasi-Armendariz skew monoid rings
Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...
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Let S be a cancellative monoid with quotient group of torsion-free rank a. We show that the monoid ring R[S] is a Hilbert ring if and only if the polynomial ring R[{ X, },s/] is a Hilbert ring, where |/| = a. Assume that R is a commutative unitary ring and G is an abelian group. The first research problem listed in [K, Chapter 7] is that of determining equivalent conditions in order that the gr...
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Cazaran and Kelarev [2] have given necessary and sufficient conditions for an ideal to be the principal; further they described all finite factor rings Zm[X1, · · · , Xn]/I, where I is an ideal generated by an univariate polynomial, which are commutative principal ideal rings. But in [3], Cazaran and Kelarev characterize the certain finite commutative rings as a principal ideal rings. Though, t...
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A rst explicit connection between nitely presented commutative monoids and ideals in polynomial rings was used 1958 by Emelichev yielding a solution to the word problem in commutative monoids by deciding the ideal membership problem. The aim of this paper is to show in a similar fashion how congruences on monoids and groups can be characterized by ideals in respective monoid and group rings. Th...
متن کاملAlgebraic K-theory of Monoid Rings
Are all finitely generated projective k[t1, . . . , td]-modules free for an arbitrary field k and arbitrary d ∈ N? This question, set in Serre’s famous paper FAC in 1955, inspired an enormous activity of algebraists worldwide. The activity culminated in two independent confirmations of the question in 1976 by Quillen and Suslin. In the meanwhile the algebraic K-theory was created, in which one ...
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ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 1989
ISSN: 0214-1493
DOI: 10.5565/publmat_33189_09