Primary decompositions of unital locally matrix algebras

Autor:	Oksana Bezushchak, Bogdana Oliynyk
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	locally matrix algebra primary decomposition steinitz number tensor product clifford algebra Mathematics QA1-939
Zdroj:	Bulletin of Mathematical Sciences, Vol 10, Iss 1, Pp 2050006-1-2050006-7 (2020)
Druh dokumentu:	article
ISSN:	1664-3607 1664-3615 16643607
DOI:	10.1142/S166436072050006X
Popis:	We construct a unital locally matrix algebra of uncountable dimension that (1) does not admit a primary decomposition, (2) has an infinite locally finite Steinitz number. It gives negative answers to questions from [V. M. Kurochkin, On the theory of locally simple and locally normal algebras, Mat. Sb., Nov. Ser. 22(64)(3) (1948) 443–454; O. Bezushchak and B. Oliynyk, Unital locally matrix algebras and Steinitz numbers, J. Algebra Appl. (2020), online ready]. We also show that for an arbitrary infinite Steinitz number s there exists a unital locally matrix algebra A having the Steinitz number s and not isomorphic to a tensor product of finite-dimensional matrix algebras.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/aa6078a60c6742d7bbe7b548f93bfead Zobrazit plný text záznamu View record in DOAJ