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Varieties with a countable number of subquasivarieties. (English. Russian original) Zbl 0573.08008

Sib. Math. J. 25, 461-473 (1984); translation from Sib. Mat. Zh. 25, No. 3(145), 148-163 (1984).
The lattice of subquasivarieties of an arbitrary quasivariety of universal algebras is called its Q-lattice. In the present paper varieties of rings and semigroups with at most countable Q-lattices are studied. The author succeeds in describing all varieties of locally finite semigroups and all varieties of rings having a countable Q- lattice. The paper is a sequel to the author’s publication in Sib. Mat. Zh. 22, No.6, 168-187 (1981; Zbl 0491.08011).
Reviewer: H.K.Kaiser

MSC:

08C15 Quasivarieties
20M07 Varieties and pseudovarieties of semigroups
08B15 Lattices of varieties
16Rxx Rings with polynomial identity

Citations:

Zbl 0491.08011
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References:

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