A new class of unique product monoids with applications to ring theory

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 s...

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Bibliographic Details
Published in:Semigroup forum 2009-03, Vol.78 (2), p.210-225
Main Authors: Marks, Greg, Mazurek, Ryszard, Ziembowski, Michał
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Research Article
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Summary: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.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-008-9063-7