Varieties of idempotent groupoids with small clones

• Autorzy: J. Gałuszka
• Języki publikacji: EN

Abstrakty

EN

We give an equational description of all idempotent groupoids with at most three essentially n-ary term operations.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 81
• Numer: 1
• Strony: 63-87

Daty

wydano

1999

otrzymano

1998-01-12

poprawiono

1999-01-02

Twórcy

autor

J. Gałuszka

• Institute of Mathematics, Silesian Technical University, 44-100 Gliwice, Poland

Bibliografia

• [1] J. Berman, Free spectra of 3-element algebras, in: Universal Algebra and Lattice Theory (Puebla, 1982), Lecture Notes in Math. 1004, Springer, Berlin, 1983, 10-53.
• [2] B. Csákány, All minimal clones on the three-element set, Acta Cybernet. 6 (1983), 227-238.
• [3] B. Csákány, On affine spaces over prime fields, Acta Sci. Math. (Szeged) 37 (1975), 33-36.
• [4] J. Dudek, Another unique minimal clone, to appear.
• [5] J. Dudek, On binary polynomials in idempotent commutative groupoids, Fund. Math. 120 (1984), 187-191.
• [6] J. Dudek, On minimal extension of sequences, Algebra Universalis 23 (1986), 308-312.
• [7] J. Dudek, On varieties of groupoid modes, Demonstratio Math. 27 (1994), 815-828.
• [8] J. Dudek, Small idempotent clones I, Czechoslovak Math. J. 48 (1998), 105-118.
• [9] J. Dudek, The minimal extension of the sequence (0,0,3), Algebra Universalis 29 (1992), 419-436.
• [10] J. Dudek, The unique minimal clone with three essentially binary operation, ibid. 27 (1990), 261-269.
• [11] J. Dudek, Varieties of idempotent commutative groupoids, Fund. Math. 120 (1984), 193-204.
• [12] G. Grätzer, Composition of functions, in: Proc. Conf. on Universal Algebra (Kingston, Ont., 1969), Queen's University, Kingston, Ont., 1970, 1-106.
• [13] G. Grätzer, Universal Algebra, Springer, Berlin, 1979.
• [14] G. Grätzer and A. Kisielewicz, A survey of some open problems on $p_n$-sequences and free spectra of algebras and varieties, in: Universal Algebra and Quasigroup Theory, A. Romanowska and J. D. H. Smith (eds.), Heldermann, Berlin, 1992, 57-88.
• [15] G. Grätzer and R. Padmanabhan, On idempotent, commutative and nonassociative groupoids, Proc. Amer. Math. Soc. 28 (1971), 75-80.
• [16] A. Kisielewicz, On idempotent algebra with $p_n = 2n$, Algebra Universalis 23 (1981), 313-323.
• [17] A. Kisielewicz, Characterization of $p_n$-sequences for nonidempotent algebras, J. Algebra 108 (1987), 102-115.
• [18] E. Marczewski, Independence and homomorphisms in abstract algebras, Fund. Math. 50 (1961), 45-61.
• [19] P. P. Pálfy, Minimal clones, Preprint No. 27/1984, Math. Inst. Hungar. Acad. Sci.
• [20] J. Płonka, On algebras with at most n distinct n-ary operations, Algebra Universalis 1 (1971), 80-85.
• [21] J. Płonka, On equational classes of abstract algebras defined by regular equations, Fund. Math. 64 (1969), 241-247.
• [22] W. Sierpiński, Sur les fonctions de plusieurs variables, ibid. 33 (1945), 169-173.