The structure of block matrices. I. Factorizations in the rings of the block matrices

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Vasyl’ Petrychkovych

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

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Nataliia Dzhaliuk

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine
 

March 12, 2019 at 15:05 in Lecture Room 377

Abstract of talk

We investigate equivalences, factorizations, and matrix unilateral and bilateral equations in the rings of the block matrices. In the first part, we consider factorizations of the block matrices, in particular, the block triangular and the block diagonal matrices over integral domains of finitely generated principal ideals. Conditions for existence and uniqueness up to the association of the factorizations in such rings are established.