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On semi-simple locally finite algebras. (Russian) Zbl 0558.16012

Let R be a regular locally finite algebra. The author proves that every finite subset of R is a subset of some semi-simple finite dimensional subalgebra if R satisfies one of the following conditions: i) R is a countably generated algebra of uniform index n; (ii) R is an LBD-algebra; iii) R is a PI-algebra.
Reviewer: Yu.N.Mal’tsev

MSC:

16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16Rxx Rings with polynomial identity
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16P10 Finite rings and finite-dimensional associative algebras
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