Almost simple algebras. (English. Russian original) Zbl 0839.08001

Algebra Logic 32, No. 5, 289-299 (1993); translation from Algebra Logika 32, No. 5, No. 5, 537-555 (1993).
Several generalizations of simple algebras have been studied in the literature. In particular, the author introduced quasisimple algebras [“On quasisimple algebras” (Russian), in: Studies of algebraic systems vs. properties of their subsystems, 108-118 (Sverdlovsk, 1987)] and, in a joint paper with A. J. Denisov, \(p\)-pseudosimple algebras [Algebra Logika 31, No. 6, 637-654 (1992; Zbl 0804.08002)]. In the present paper he defines and investigates further generalizations: \(p\)-quasisimple algebras (which contain the two above-mentioned classes) and \(p\)-separable algebras (lying between the \(p\)-pseudosimple and the \(p\)-quasisimple algebras). A number of structure theorems are obtained involving, e.g., the congruence lattice, quasivarieties and some model theory.


08A30 Subalgebras, congruence relations
08C15 Quasivarieties
03C60 Model-theoretic algebra


Zbl 0804.08002
Full Text: DOI


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