On primary decomposition of modules

TL;DR

This paper extends algorithms for primary decomposition of modules in commutative algebra, providing new proofs and implementations in Singular, enhancing computational tools for algebraic geometry.

Contribution

It generalizes existing algorithms for primary decomposition to free modules and supplies rigorous proofs for key theorems, improving theoretical and computational methods.

Findings

Algorithms for primary decomposition are implemented in Singular.

New proofs for important theorems in primary decomposition.

Enhanced computational tools for algebraic geometry.

Abstract

Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also filled some gaps by providing proofs of important theorems(2.9, 2.12, 2.13) appeared in [EHV]. All these algorithms are programmed and implemented in {\sc Singular}.