Indecomposable and isomorphic objects in the category of monomial matrices over a local ring

Abstract

We study the indecomposability and isomorphism of objects from the category of monomial matrices $\mathrm{M}\mathrm{m}\mathrm{a}\mathrm{t}(K)$ over a commutative local principal ideal ring $K$ (whose objects are square monomial matrices and the morphisms from $X$ to $Y$ are the matrices $C$ such that $XC = CY$). We also study the subcategory $\mathrm{M}\mathrm{m}\mathrm{a}\mathrm{t}_0(K)$ of the category $\mathrm{M}\mathrm{m}\mathrm{a}\mathrm{t}(K)$ with the same objects and only those morphisms that are monomial matrices.