The ascending chain condition for principal left or right ideals of skew generalized power series 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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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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We study prime ideals in skew power series rings T := R[[y; τ, δ]], for suitably conditioned complete right noetherian rings R, automorphisms τ of R, and τ -derivations δ of R. Such rings were introduced by Venjakob, motivated by issues in noncommutative Iwasawa theory. Our main results concern “Cutting Down” and “Lying Over.” In particular, assuming that τ extends to a compatible automorphsim ...
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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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We study skew inverse power series extensions R[[y−1; τ, δ]], where R is a noetherian ring equipped with an automorphism τ and a τ -derivation δ. We find that these extensions share many of the well known features of commutative power series rings. As an application of our analysis, we see that the iterated skew inverse power series rings corresponding to nth Weyl algebras are complete, local, ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.03.040