Special properties of generalized power series
Given a commutative ring \(R\) and a strictly ordered monoid \((S, \leq)\), the generalized power series ring \(A = RS, \leq\) is defined to be the set of all maps \(f : S \to R\) such that support\((f) = \{s \in S : f(s) \neq 0\}\) is artinian and narrow. The addition and multiplication on \(A\) are defined appropriately. -- The purpose of this paper is to investigate the validity of various results about power series rings in the case of generalized power series rings. One of the many interesting results in this paper is that: If \((S, \leq)\) is artinian and narrow as an ordered set and if \(S\) is a free monoid then for a field \(R\), the generalized power series ring \(A = RS, \leq\) is an UFD. There are many other results of similar nature. Of particular interest among them are the results on seminormality.
scientific article; zbMATH DE number 763961