Algebra & Combinatorics Research Group  |  Texas A&M University





A&C Seminar

Working Seminar
   in Algebra

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A&C Seminar:  Fall 2008, Fridays, Milner 317, 3:00–3:50 p.m.

November 21 Scott Chapman (Sam Houston State University)
3:00–3:50 An Introduction to the Theory of Non-unique Factorizations
Abstract:   The study of unique factorization domains (or UFDs) played an important role in the development of Algebraic Number Theory and Commutative Algebra. In this talk, we consider integral domains and monoids which do not satisfy the unique factorization criteria. Over the past 30 years, the algebraic and combinatorial aspects of non-unique factorizations has been widely studied. After reviewing many of the basic results in this area, I will focus on several classes of monoids (numerical monoids, congruence monoids and block monoids) which have appeared frequently in the recent mathematical literature.