A characterization of seminormal C-monoids

Abstract

It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class group of Krull monoids. We prove that a C-monoid is seminormal if and only if its reduced class semigroup is a union of groups. Based on this characterization we establish a criterion (in terms of the class semigroup) when seminormal C-monoids are half-factorial.2010 Mathematics Subject Classification. 20M13, 13A05, 13A15, 13F05, 13F45.

Length-factoriality in commutative monoids and integral domains

“…An integral domain is called halffactorial if its multiplicative monoid is half-factorial. Half-factorial monoids and domains have been systematically investigated during the last six decades in connection with algebraic number theory, combinatorics, and commutative algebra: from work that appeared more than two decades ago, such as [9,17,20,51], to more recent literature, including [26,32,35,42,[46][47][48]. The term "half-factorial" was coined by Zaks in [51].…”