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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

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

Abstract

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 Nm described below. In [2], this fact was proved for m = 2.

Bibliography

  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, pn-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 pn-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.
Colloquium Mathematicum
1996/71/2
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Pages:
335-338
Main language of publication
English
Received
1995-06-03
Accepted
1995-10-11
Published
1996
Exact and natural sciences