On primary decompositions of unital locally matrix algebras

2019/11/25 by Bezushchak, Oksana, Oliynyk, Bogdana · 1 citation
#03C05 #03C60 #11E88 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1911.10887

Abstract

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 \citeBezOl and \citeKurochkin. 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.

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