The subalgebra lattice of a finite algebra

• Autorzy: Konrad Pióro
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.

Słowa kluczowe

EN

Directed hypergraph; Finite algebra; Finite lattice; Subalgebra; Subalgebra lattice; Distributive lattice; Partial

Kategorie tematyczne

• 06B05: Structure theory
• 06B15: Representation theory
• 06D05: Structure and representation theory
• 08A55: Partial algebras
• 05C90: Applications
• 06B99: None of the above, but in this section
• 08A30: Subalgebras, congruence relations
• 05C65: Hypergraphs
• 05C99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 7
• Strony: 1052-1108

Daty

wydano

2014-07-01

online

2014-04-03

Twórcy

autor

Konrad Pióro

• University of Warsaw

Bibliografia

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• [11] Pióro K., On the subalgebra lattice of unary algebras, Acta Math. Hungar., 1999, 84(1–2), 27–45 http://dx.doi.org/10.1023/A:1006694618179
• [12] Pióro K., On connections between hypergraphs and algebras, Arch. Math. (Brno), 2000, 36(1), 45–60
• [13] Pióro K., On some non-obvious connections between graphs and unary partial algebras, Czechoslovak Math. J., 2000, 50(125), 295–320 http://dx.doi.org/10.1023/A:1022418818272
• [14] Pióro K., On subalgebra lattices of a finite unary algebra I, Math. Bohem., 2001, 126(1), 161–170

Identyfikatory

DOI

10.2478/s11533-013-0390-x