Year: 2025
Type: article
Abstract: In this paper, we extend classical results on unimodular elements and the completability of unimodular rows in torsion-free pure projective modules over commutative Noetherian rings. We establish a stable freeness criterion that characterises global completability in terms of module-theoretic properties, generalising Serre-Plumstead-type results for a broader class of modules that are not necessarily free. Applications to linear codes over rings are investigated, showing strong structural and distance properties. This work generalises the local-global principle for row completability beyond projective modules and provides a new framework for understanding module decompositions in the algebraic case. Applications include the construction of generator matrices in coding theory over rings, where unimodular rows encode critical structural and distance properties.
Source: Mitteilungen Klosterneuburg
DOI: 10.61586/fybuk
Authors: Pooja Gupta, Ratnesh Kumar Mishra
Institution: National Institute of Technology Jamshedpur
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411538706