Decompositions of Monomial Ideals in Real Semigroup Rings

2012/01/14 by Ingebretson, Daniel, Sather-Wagstaff, Sean
#13C05 #13F20 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.3040

Abstract

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[ℝ_{≥ 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.

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