A note on arithmetics in semigroups
Kentaro Murata · Proceedings of the Japan Academy Series A Mathematical Sciences · 1980
Considering a modular closure of an ideal system in a semigroup, we can define, following [1], a conductor of an order contained in (and equivalent to) a regular maximal order of the semigroup.The aim of this note is to introduce, by the conductor, regular ideals, regular v- ideals and regular subsets of the semigroup, and to give factorization theorems for these ideals and subsets by using the results in [2], [5].Our results are applicable to the case of rings, if we take the "module- generation" as a modular closure.