Almost simple algebras
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 \textit{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.
scientific article; zbMATH DE number 738962