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

J. Dudek

Colloquium Mathematicae (1996)

  • Volume: 71, Issue: 2, page 335-338
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Dudek, J.. "The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz." Colloquium Mathematicae 71.2 (1996): 335-338. <http://eudml.org/doc/210446>.

@article{Dudek1996,
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 $N_m$ described below. In [2], this fact was proved for m = 2.},
author = {Dudek, J.},
journal = {Colloquium Mathematicae},
keywords = {totally commutative idempotent groupoids; essentially binary polynomials},
language = {eng},
number = {2},
pages = {335-338},
title = {The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz},
url = {http://eudml.org/doc/210446},
volume = {71},
year = {1996},
}

TY - JOUR
AU - Dudek, J.
TI - The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz
JO - Colloquium Mathematicae
PY - 1996
VL - 71
IS - 2
SP - 335
EP - 338
AB - 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.
LA - eng
KW - totally commutative idempotent groupoids; essentially binary polynomials
UR - http://eudml.org/doc/210446
ER -

References

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  1. [1] J. Dudek, Variety of idempotent commutative groupoids, Fund. Math. 120 (1984), 193-204. Zbl0546.20049
  2. [2] J. Dudek, On the minimal extension of sequences, Algebra Universalis 23 (1986), 308-312. Zbl0627.08001
  3. [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. [4] G. Grätzer, Composition of functions, in: Proc. Conference on Universal Algebra, Kingston, 1969, Queen's Univ., Kingston, Ont., 1970, 1-106. 
  5. [5] G. Grätzer, Universal Algebra, 2nd ed., Springer, New York, 1979. 
  6. [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. Zbl0772.08001

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