Abstract
In this paper, some special varieties which generalize Jónsson–Tarski algebras are considered. We prove that every nontrivial algebra from such a variety is term infinite and contains infinitely many distinct proper diagonal term operations of every arity.
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Dudek J.: Remarks on algebras having two bases of different cardinalities. Colloq. Math. 22, 197–200 (1971)
Dudek J.: On universal algebras having bases of different cardinalities. Colloq. Math. 42, 111–114 (1979)
Dudek, J., Marczak, A.W.: Płonka diagonal algebras (in press)
Goetz, A., Ryll-Nardzewski, C.: On bases of abstract algebras. Bull. Polish Acad. Sci. Math. 8, 157–161 (1960)
Grätzer, G.: Universal Algebra, 2nd edn. Springer, New York (1979)
Jónsson, B., Tarski, A.: Two general theorems concerning free algebras. In: The Summer Meeting in Seattle, p. 554. Bull. Amer. Math. Soc. 62, 541–611 (1956)
Jónsson, B., Tarski, A.: On two properties of free algebras. Math. Scand. 9, 95–101 (1961)
Kisielewicz, A.: On algebras with bases of different cardinalities. Fund. Math. 133, 147–154 (1989)
Marczewski, E.: Independence and homomorphisms in abstract algebras. Fund. Math. 50, 45–61 (1961)
Marczewski, E.: Independence in abstract algebras. Results and problems. Colloq. Math. 14, 169–188 (1966)
Narkiewicz, W.: Remarks on abstract algebras having bases with different number of elements. Colloq. Math. 15, 11–17 (1966)
Płonka, J.: Diagonal algebras and algebraic independence. Bull. Polish Acad. Sci. Math. 12, 729–733 (1964)
Płonka, J: Diagonal algebras. Fund. Math. 58, 309–321 (1966)
Płonka, J: On the arity of idempotent reducts of groups, Colloq. Math. 21, 35–37 (1970)
Świerczkowski, S.: On isomorphic free algebras. Fund. Math. 50, 35–44 (1961)
Taylor, W.: Some interesting identities. An. Inst. Mat. Univ. Nac. Autónoma México 20, 127–156 (1980)
Taylor, W.: The clone of a topological space. In: Research and Exposition in Mathematics, vol. 13. Heldermann, Berlin (1986)
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Presented by E. Kiss.
Józef Dudek died unexpectedly in 2008. Some ideas of this paper are based on his suggestions.
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Dudek, J., Marczak, A.W. On Cantor identities. Algebra Univers. 68, 237–247 (2012). https://doi.org/10.1007/s00012-012-0204-1
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DOI: https://doi.org/10.1007/s00012-012-0204-1