Gr\"{o}bner bases and syzygy theorem for direct product of principal ideal rings

TL;DR

This paper extends Hilbert's syzygy theorem to finitely generated modules over polynomial rings constructed from direct products of principal ideal rings, broadening the theorem's applicability.

Contribution

It provides new versions of Hilbert's syzygy theorem tailored for modules over polynomial rings over direct product of principal ideal rings.

Findings

Extended Hilbert's syzygy theorem to new algebraic structures

Established syzygy properties for modules over these rings

Enhanced understanding of module resolutions in this context

Abstract

In this paper we give versions of Hilbert's syzygy theorem for finitely generated modules over polynomial rings over direct product of principal ideal rings.