## 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.

### MSC:

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

Zbl 0804.08002
Full Text:

### References:

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