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It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
87-100
Opis fizyczny
Daty
wydano
2002
otrzymano
2002-04-19
poprawiono
2002-07-02
Twórcy
autor
- Institute of Mathematics, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
Bibliografia
- [1] G. Bińczak, A characterization theorem for weak varieties, Algebra Universalis 45 (2001), 53-62.
- [2] P. Burmeister, A Model - Theoretic Oriented Approach to Partial Algebras, Akademie-Verlag, Berlin 1986.
- [3] G. Grätzer, Universal Algebra, (the second edition), Springer-Verlag, New York 1979.
- [4] H. Höft, Weak and strong equations in partial algebras, Algebra Universalis 3 (1973), 203-215.
- [5] E. Jacobs and R. Schwabauer, The lattice of equational classes of algebras with one unary operation, Amer. Math. Monthly 71 (1964), 151-155.
- [6] L. Rudak, A completness theorem for weak equational logic, Algebra Universalis 16 (1983), 331-337.
- [7] L. Rudak, Algebraic characterization of conflict-free varieties of partial algebras, Algebra Universalis 30 (1993), 89-100.
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1049