PreprintCC BY 4.0arXiv
Primary decompositions via exponent matrices
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.
Related
- On the Unified Generalized q-Stirling Matrices and Their Matrix Decompositions
- Unique direct-sum decompositions of infinite-dimensional unitary representations of the infinite dihedral group via real CMV matrices
- Minor-Order Exponent Profiles of Oscillatory Matrices
- Exponent Profiles of Oscillatory Matrices under Matrix and Inverse Sparsity
- Primary Decompositions in Lorentz-Covariant Rings
BibTeX
@misc{miller2026primary,
title = {{Primary decompositions via exponent matrices}},
author = {Jacob Miller},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25409},
eprint = {2609.25409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25409},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Primary decompositions via exponent matrices
AU - Jacob Miller
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25409
UR - https://arxiv.org/abs/2609.25409
AB - 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.
ER -