SPECIAL PROPERTIES OF MODULES OF GENERALIZED POWER SERIES

Abstract

Let $R$ be a ring, $M$ a right $R$-module and $(S,\leq)$ a strictly ordered monoid. In this paper, a necessary and sufficient condition is given for modules under which $[[M^{S,\leq}]]_{[[R^{S,\leq}]]}$, the module of generalized power series with coefficients in $M$ and exponents in $S$ is a reduced, Baer, PP. quasi-Baer module, respectively.