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On primary decompositions of unital locally matrix algebras
- Publication Year :
- 2019
-
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 \cite{BezOl} and \cite{Kurochkin}. 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.
- Subjects :
- Mathematics - Rings and Algebras
03C05, 03C60, 11E88
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1911.10887
- Document Type :
- Working Paper