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arXiv · 2609.25409

Primary decompositions via exponent matrices

Jacob Miller
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Abstract

In this paper we present a new result that exhibits in a non-recursive fashion a primary decomposition of any monomial ideal. Our result is derived from the classical quotient-sum recursive procedure for determining a primary decomposition of any proper ideal in a commutative Noetherian ring. We also show how our result can be used as an algorithm for producing a primary decomposition directly from the exponent vectors of the minimal generators of the ideal.

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Jacob Miller. 2026-09-21. Primary decompositions via exponent matrices. https://arxiv.org/abs/2609.25409

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