On the monoid algebra associated to the monomial characters of a finite group

Abstract

Given a finite group G, we study the monoid algebra RG, over a field K, generated by the monomial characters of G. In particular, we note  that the integral closure of RG is contained in the algebra generated by those characters χ for which their associated Artin L-function L(s,  χ) is holomorphic at s0 ∈ C \ {1}. Also, we discuss the supercharacter theoretic case