New York Journal of Mathematics
Volume 23 (2017) 1273-1293


Ryszard Mazurek and Kamal Paykan

Simplicity of skew generalized power series rings

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Published: September 19, 2017
Keywords: Skew generalized power series ring, simple ring, (S, ω )-simple ring, strictly ordered monoid.
Subject: Primary 16S35, 16W22, 16W60, 16U70; Secondary 06F05, 06F15

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 skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal'cev-Neumann series rings, the "untwisted" versions of all of these, and generalized power series rings. In this paper we obtain necessary and sufficient conditions on R, S and ω such that the skew generalized power series ring R[[S,ω ]] is a simple ring. As particular cases of our general results we obtain new theorems on skew monoid rings, skew Mal'cev-Neumann series rings and generalized power series rings, as well as known characterizations for the simplicity of skew Laurent polynomial rings, skew Laurent series rings and skew group rings.


The research of Ryszard Mazurek was supported by the Bialystok University of Technology grant S/WI/1/2014.

Author information

Ryszard Mazurek:
Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland

Kamal Paykan:
Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran