Rings of generalized power series. II: Units and zero-divisors
[For part I see Abh. Math. Semin. Univ. Hamb. 61, 15-33 (1991; Zbl 0751.13005).] Consider a strictly ordered monoid \(S\) and a commutative ring \(R\) with unit element. A generalized power series with coefficients in \(R\) and exponents in \(S\) is a mapping \(f:S \to R\) having artinian and narrow support \((\text{supp} (f))\), that is every strictly decreasing sequence in \(\text{supp} (f)\) is finite and every subset of pairwise order incomparable elements of \(\text{supp} (f)\) is finite. The pointwise addition defines an addition in generalized power series and the properties on \(\text{supp} (f)\) permit to define a convolution product. The set \(A\) of generalized power series becomes a commutative ring with unit element. In several papers (e.g. part I of this paper) the author studied properties of the ring \(A\); this paper concerns units and zero divisors, and quasi-cancellative rings.
scientific article; zbMATH DE number 645071