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arXiv · 1201.3040

Decompositions of Monomial Ideals in Real Semigroup Rings

Daniel Ingebretson·Sean Sather-Wagstaff
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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[\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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Daniel Ingebretson, Sean Sather-Wagstaff. 2012-05-18. Decompositions of Monomial Ideals in Real Semigroup Rings. https://arxiv.org/abs/1201.3040

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