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Factorizations in the rings of the block matrices Vasyl' Petrychkovych, Nataliia Dzhaliuk Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the NAS of Ukraine, Department of Algebra, 3b Naukova Str., 79060, L'viv, Ukraine Аннотация: The factorizations in the rings of the block triangular and the block diagonal matrices over an integral domain of finitely generated principal ideals are described. Conditions for existence and uniqueness up to the association of the factorizations in such rings are established. The construction of the factorizations of matrices is reduced to the factorizations of diagonal blocks of the block triangular matrices and the solving of the linear Sylvester matrix equations. Ключевые слова и фразы: ring of matrices, block matrix, factorization, matrix equation.  Полный текст:
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Тип публикации: Статья MSC: 15A21, 15A24 Поступила в редакцию: 10.01.2017 Язык публикации: английский Образец цитирования: Vasyl' Petrychkovych, Nataliia Dzhaliuk, “Factorizations in the rings of the block matrices”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 3, 
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