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

Colloquium Mathematicae (1996)

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

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topDudek, 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

top- [1] J. Dudek, Variety of idempotent commutative groupoids, Fund. Math. 120 (1984), 193-204. Zbl0546.20049
- [2] J. Dudek, On the minimal extension of sequences, Algebra Universalis 23 (1986), 308-312. Zbl0627.08001
- [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. Zbl0772.08001

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