On Von Neumann Regular Rings of Skew Generalized Power Series |
| |
Authors: | R. Mazurek M. Ziembowski |
| |
Affiliation: | 1. Faculty of Computer Science , Bialystok Technical University , Bia?ystok, Poland mazurek@pb.bialystok.pl;3. ?ochów, Poland |
| |
Abstract: | In this paper we introduce a construction called the skew generalized power series ring R[[S, ω]] with coefficients in a ring R and exponents in a strictly ordered monoid S which extends Ribenboim's construction of generalized power series rings. In the case when S is totally ordered or commutative aperiodic, and ω(s) is constant on idempotents for some s ∈ S?{1}, we give sufficient and necessary conditions on R and S such that the ring R[[S, ω]] is von Neumann regular, and we show that the von Neumann regularity of the ring R[[S, ω]] is equivalent to its semisimplicity. We also give a characterization of the strong regularity of the ring R[[S, ω]]. |
| |
Keywords: | Artinian and narrow set Semisimple ring Skew generalized power series ring Strictly ordered monoid Von Neumann regular ring |
|
|