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Semigroup Forum

, 78:210 | Cite as

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

  • Greg Marks
  • Ryszard Mazurek
  • Michał Ziembowski
Research article

Abstract

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.

Keywords

Artinian narrow unique product monoid Unique product monoid Skew generalized power series ring Reduced ring Armendariz ring 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Greg Marks
    • 1
  • Ryszard Mazurek
    • 2
  • Michał Ziembowski
  1. 1.Department of Mathematics and Computer ScienceSt. Louis UniversitySt. LouisUSA
  2. 2.Faculty of Computer ScienceBialystok Technical UniversityBiałystokPoland

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