The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz

• Autorzy: J. Dudek
• Języki publikacji: EN

Abstrakty

EN

The main result of this paper is a description of totally commutative idempotent groupoids. In particular, we show that if an idempotent groupoid (G,·) has precisely m ≥ 2 distinct essentially binary polynomials and they are all commutative, then G contains a subgroupoid isomorphic to the groupoid $N_m$ described below. In [2], this fact was proved for m = 2.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 71
• Numer: 2
• Strony: 335-338

Daty

wydano

1996

otrzymano

1995-06-03

poprawiono

1995-10-11

Twórcy

autor

J. Dudek

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] J. Dudek, Variety of idempotent commutative groupoids, Fund. Math. 120 (1984), 193-204.
• [2] J. Dudek, On the minimal extension of sequences, Algebra Universalis 23 (1986), 308-312.
• [3] J. Dudek, $p_n$-sequences. The minimal extension of sequences (Abstract), presented at the Conference on Logic and Algebra dedicated to Roberto Magari on his 60th birthday, Pontignano (Siena), 26-30 April 1994, 1-6.
• [4] G. Grätzer, Composition of functions, in: Proc. Conference on Universal Algebra, Kingston, 1969, Queen's Univ., Kingston, Ont., 1970, 1-106.
• [5] G. Grätzer, Universal Algebra, 2nd ed., Springer, New York, 1979.
• [6] 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.