%0 Journal Article
%T Decompositions of Monomial Ideals in Real Semigroup Rings
%A Daniel Ingebretson
%A Sean Sather-Wagstaff
%J Mathematics
%D 2012
%I arXiv
%X Irreducible decompositions of monomial ideals in polynomial rings over a field are well-understood. In this paper, we investigate decompositions in the set of monomial ideals in the semigroup ring A[\mathbb{R}_{\geq 0}^d] where A is an arbitrary commutative ring with identity. We classify the irreducible elements of this set, which we call m-irreducible, and we classify the elements that admit decompositions into finite intersections of m-irreducible ideals.
%U http://arxiv.org/abs/1201.3040v2