2018
Том 70
№ 6

# 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.

Citation Example: Bondarenko V. M., Bortos M. Yu. Indecomposable and isomorphic objects in the category of monomial matrices over a local ring // Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 889-904.