Group Actions on Polynomial and Power Series Rings
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چکیده
منابع مشابه
Nilpotent Elements in Skew Polynomial Rings
Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...
متن کاملSimplicity 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...
متن کاملON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS
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...
متن کاملOn Nilpotent Power Series with Nilpotent Coefficients
Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...
متن کاملCHAPTER IV Groups and Group Actions
This chapter develops the basics of group theory, with particular attention to the role of group actions of various kinds. The emphasis is on groups in Sections 1–3 and on group actions starting in Section 6. In between is a two-section digression that introduces rings, fields, vector spaces over general fields, and polynomial rings over commutative rings with identity. Section 1 introduces gro...
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تاریخ انتشار 2006