Locally finite Jonsson conditional varieties and the conditional rational equivalence. (English. Russian original) Zbl 0920.08004
Sib. Math. J. 39, No. 4, 816-820 (1998); translation from Sib. Mat. Zh. 39, No. 4, 942-948 (1998).
A notion of a locally finite Jonsson conditional variety is introduced. In the author’s article [Algebra Logika 37, No. 4, 432-459 (1998; Zbl 0913.08008)], for two given conditional varieties, he studied the relationship between the isomorphism of the embedding categories of the varieties and the conditional rational equivalence of these varieties (there, the last term is translated as “conditioned rational equivalence”); as an application, abstract invariants were described for the classes of conditionally rationally equivalent finite algebras and for the classes of similar finite algebras. In the article under review, abstract invariants are given for two locally finite Jonsson conditional varieties that are conditionally rationally equivalent.
Reviewer: A.N.Ryaskin (Novosibirsk)
MSC:
08C05 | Categories of algebras |
08B05 | Equational logic, Mal’tsev conditions |
08B10 | Congruence modularity, congruence distributivity |
Keywords:
universal algebra; conditional identity; conditional rational equivalence; conditioned rational equivalence; conditional variety; locally finite Jonsson conditional variety; similar algebras; discriminator termCitations:
Zbl 0913.08008References:
[1] | A. G. Pinus, ”On conditional terms and identities on universal algebras,” Siberian Adv. Math.,8, No. 2, 96–109 (1998). · Zbl 0924.08005 |
[2] | A. G. Pinus, ”Calculus of conditional identities and conditionally rational equivalence,” Algebra i Logika (to appear). · Zbl 0913.08008 |
[3] | M. Morley and R. Vaught, ”Homogeneous universal models,” Math. Scand.,11, No. 1, 37–57 (1963). · Zbl 0112.00603 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.