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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1049,
author = {Grzegorz Bi\'nczak},
title = {Equational bases for weak monounary varieties},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {22},
year = {2002},
pages = {87-100},
zbl = {1037.08004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1049}
}
Grzegorz Bińczak. Equational bases for weak monounary varieties. Discussiones Mathematicae - General Algebra and Applications, Tome 22 (2002) pp. 87-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1049/
[000] [1] G. Bińczak, A characterization theorem for weak varieties, Algebra Universalis 45 (2001), 53-62. | Zbl 1039.08002
[001] [2] P. Burmeister, A Model - Theoretic Oriented Approach to Partial Algebras, Akademie-Verlag, Berlin 1986. | Zbl 0598.08004
[002] [3] G. Grätzer, Universal Algebra, (the second edition), Springer-Verlag, New York 1979.
[003] [4] H. Höft, Weak and strong equations in partial algebras, Algebra Universalis 3 (1973), 203-215. | Zbl 0287.08003
[004] [5] E. Jacobs and R. Schwabauer, The lattice of equational classes of algebras with one unary operation, Amer. Math. Monthly 71 (1964), 151-155. | Zbl 0117.26003
[005] [6] L. Rudak, A completness theorem for weak equational logic, Algebra Universalis 16 (1983), 331-337. | Zbl 0519.08006
[006] [7] L. Rudak, Algebraic characterization of conflict-free varieties of partial algebras, Algebra Universalis 30 (1993), 89-100. | Zbl 0810.08003