Transforming a matrix into a standard form

TL;DR

This paper proves that matrices with entries in a subgroup of units of a commutative ring can be transformed into a standard form, improving existing proofs in the literature.

Contribution

It introduces a method to convert such matrices into a standard form, enhancing previous results in the theory of matrices over rings.

Findings

Matrices with entries in a subgroup of units are equivalent to a standard form

Improved proof of a key theorem in matrix theory over rings

Enhanced understanding of matrix transformations in algebraic structures

Abstract

We show that every matrix all of whose entries are in a fixed subgroup of the group of units of a commutative ring with identity is equivalent to a standard form. As a consequence, we improve the proof of Theorem 5 in D. Best, H. Kharaghani, H. Ramp [Disc. Math. 313 (2013), 855--864].