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Polynomials in idempotent commutative groupoids

100%

Dudek J.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS 1. Introduction......................................................................5 2. Terminology......................................................................7 3. Applied results.................................................................8 4. Nonmedial groupoids.....................................................10 5. Sterner quasigroups......................................................13 6. Near-semilattices...........................................................17 7. Totally commutative groupoids.......................................21 8. Some lemmas on idempotent algebras..........................27 9. Ternary polynomials.......................................................29 10. Nonmedial groupoids (continued)................................33 11. Medial groupoids..........................................................39 12. Proof of Theorem 1......................................................48 13. Proof of Theorem 2......................................................48 References........................................................................52

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Affine spaces as models for regular identities

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Cho J., Dudek J.

Colloquium Mathematicum

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2002

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tom 91

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nr 1

29-38

EN

In [7] and [8], two sets of regular identities without finite proper models were introduced. In this paper we show that deleting one identity from any of these sets, we obtain a set of regular identities whose models include all affine spaces over GF(p) for prime numbers p ≥ 5. Moreover, we prove that this set characterizes affine spaces over GF(5) in the sense that each proper model of these regular identities has at least 13 ternary term functions and the number 13 is attained if and only if the model is equivalent to an affine space over GF(5).

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A polynomial characterization of nondistributive modular lattices

43%

Dudek J.

Colloquium Mathematicum

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1988

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tom 55

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nr 2

195-212

Ograniczanie wyników

2 Colloquium Mathematicum

3 Dudek J.

1 Cho J.

1 2002

1 1989

1 1988

Polynomials in idempotent commutative groupoids

Affine spaces as models for regular identities

A polynomial characterization of nondistributive modular lattices