Decompositions of Monomial Ideals in Real Semigroup Rings

Details Decompositions of Monomial Ideals in Real Semigroup Rings Decompositions of Monomial Ideals in Real Semigroup Rings

2012-01-14

arxiv.org/abs/1201.3040v1

Mathematics

Commutative Algebra

13 pages, submitted

Scientific paper

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.

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