Geodesic
Equational bases for weak monounary varieties
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 87-100

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: partial algebra, weak equation, weak variety, regular equation, regular weak equational theory, monounary algebras 
Bińczak, Grzegorz. Equational bases for weak monounary varieties. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 87-100. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a6/
@article{DMGAA_2002_22_1_a6,
     author = {Bi\'nczak, Grzegorz},
     title = {Equational bases for weak monounary varieties},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {87--100},
     year = {2002},
     volume = {22},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a6/}
}
TY  - JOUR
AU  - Bińczak, Grzegorz
TI  - Equational bases for weak monounary varieties
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2002
SP  - 87
EP  - 100
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a6/
LA  - en
ID  - DMGAA_2002_22_1_a6
ER  - 
%0 Journal Article
%A Bińczak, Grzegorz
%T Equational bases for weak monounary varieties
%J Discussiones Mathematicae. General Algebra and Applications
%D 2002
%P 87-100
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a6/
%G en
%F DMGAA_2002_22_1_a6

[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.