منابع مشابه
Commutative Monoid Rings as Hilbert Rings
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...
متن کاملOn 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...
متن کاملCodes through Monoid Rings and Encoding
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...
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 ...
متن کاملThe isomorphism problem for commutative monoid rings’
By substantial changes and corrections in Demushkin’s old paper the essentially final positive answer to the isomorphism problem for monoid rings of submonoids of Z’ is obtained. This means that the underlying monoid is shown to be determined (up to isomorphism) by the corresponding monoid ring. Thereafter the positive answer to the analogous question for the ‘dual’ objects descrete Hodge algeb...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90201-6