A new class of unique product monoids with applications to ring theory
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We introduce a class of ordered monoids defined by the existence of certain “unique products” with respect to artinian and narrow subsets of the monoid. The logical relationships between this and other significant classes of monoids are explicated with several examples. We conclude with results on skew generalized power series rings. The new class of monoids provides the appropriate setting for obtaining results on reduced rings and domains of skew generalized power series, and on analogues of Armendariz rings.
KeywordsArtinian narrow unique product monoid Unique product monoid Skew generalized power series ring Reduced ring Armendariz ring
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