The quiver of an affine monoid

Abstract

If R is a finite commutative ring, then the affine monoid of R is the monoid of all affine mappings x → ax + b on R. Alternatively, it is the semidirect product of the multiplicative monoid of R with the additive group of R. In this paper we compute the Gabriel quiver of the complex algebra of the affine monoid of any finite commutative ring.