On n-root closedness of generalized power series rings over pairs of rings
نویسندگان
چکیده
منابع مشابه
Simplicity of skew generalized power series rings
A skew generalized power series ring R[[S, ω]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are...
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Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse ske...
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Let K be a field of characteristic zero and let K((R≤0)) denote the ring of generalized power series (i.e., formal sums with well-ordered support) with coefficients in K, and non-positive real exponents. Berarducci (2000) constructed an irreducible omnific integer, in the sense of Conway (2001), by first proving that an element of K((R≤0)) that is not divisible by a monomial and whose support h...
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In this paper, using generalized partial skew versions of Armendariz rings, we study the transfer of left (right) zip property between a ring R and partial skew generalized power series rings
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Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1999
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(98)00064-4