Primary decompositions of unital locally matrix algebras
Keyword(s):
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 [Formula: see text] there exists a unital locally matrix algebra [Formula: see text] having the Steinitz number [Formula: see text] and not isomorphic to a tensor product of finite-dimensional matrix algebras.
1982 ◽
Vol 33
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pp. 351-355
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2019 ◽
Vol 19
(09)
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pp. 2050180
1980 ◽
Vol 23
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pp. 227-230
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2002 ◽
Vol 45
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pp. 499-508
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1986 ◽
Vol 29
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pp. 97-100
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2019 ◽
Vol 28
(14)
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pp. 1944006
1976 ◽
Vol 10
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pp. 165-183
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