On von Neumann regular rings of skew generalized power series

摘要

In this paper we introduce a construction called the skew generalized power series ring R[[S, omega]] 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 omega(s) is constant on idempotents for some s is an element of S {1}, we give sufficient and necessary conditions on R and S such that the ring R[[S, omega]] is von Neumann regular, and we show that the von Neumann regularity of the ring R[[S, omega]] is equivalent to its semisimplicity. We also give a characterization of the strong regularity of the ring R[[S, omega]].