ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

Covering modules by proper submodules

Khare, AP and Tikaradze, A (2021) Covering modules by proper submodules. In: Communications in Algebra .

com_alg_2021.pdf - Published Version

Download (1MB) | Preview
Official URL: https://doi.org/10.1080/00927872.2021.1959922


A classical problem in the literature seeks the minimal number of proper subgroups whose union is a given finite group. A different question, with applications to error-correcting codes and graph colorings, involves covering vector spaces over finite fields by (minimally many) proper subspaces. In this note we cover R-modules by proper submodules for commutative rings R, thereby subsuming and recovering both cases above. Specifically, we study the smallest cardinal number (Formula presented.) possibly infinite, such that a given R-module is a union of (Formula presented.) -many proper submodules. (1) We completely characterize when (Formula presented.) is a finite cardinal; this parallels for modules a 1954 result of Neumann. (2) We also compute the covering (cardinal) numbers of finitely generated modules over quasi-local rings and PIDs, recovering past results for vector spaces and abelian groups respectively. (3) As a variant, we compute the covering number of an arbitrary direct sum of cyclic monoids. Our proofs are self-contained. © 2021 Taylor & Francis Group, LLC.

Item Type: Journal Article
Publication: Communications in Algebra
Publisher: Taylor and Francis Ltd.
Additional Information: The copyright for this article belongs to Authors
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 28 Nov 2021 09:06
Last Modified: 28 Nov 2021 09:06
URI: http://eprints.iisc.ac.in/id/eprint/69956

Actions (login required)

View Item View Item