Equational bases for weak monounary varieties

• Autorzy: Grzegorz Bińczak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

partial algebra; weak equation; weak variety; regular equation; regular weak equational theory; monounary algebras

Kategorie tematyczne

• 08B05: Equational logic, Mal\cprime cev (Mal\cprime tsev) conditions
• 08A55: Partial algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 87-100

Daty

wydano

2002

otrzymano

2002-04-19

poprawiono

2002-07-02

Twórcy

autor

Grzegorz Bińczak

• 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.

Identyfikatory

DOI

10.7151/dmgaa.1049