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Algebra Logika, 2012, Volume 51, Number 2, Pages 276–284 (Mi al534)  

Semilattices of definable subalgebras. II

A. G. Pinus

Novosibirsk, Russia

Abstract: In studying derived objects on universal algebras, such as automorphisms, endomorphisms, congruences, subalgebras, etc., we are naturally interested in those that can be defined by the means of the universal algebras themselves (i.e., are definable in one sense or another) – in particular in what part of all relevant derived objects is constituted by these. It is proved that for any algebraic lattice L and any of its $0$-$1$-lower subsemilattices $L_0\subseteq L_1\subseteq L_2$, there exist a universal algebra $\mathcal A$ and an isomorphism $\varphi$ of the lattice $L$ onto the lattice $\mathrm{Sub}\mathcal A$ such that $\varphi(L_0)=\mathrm{OFSub}\mathcal A$, $\varphi(L_1)=\mathrm{POFSub}\mathcal A$, $\varphi(L_2)=\mathrm{FSub}\mathcal A$, and $\mathrm{PFSub}\mathcal A=\mathrm{FSub}\mathcal A$.

Keywords: semilattice, definable subalgebra.

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English version:
Algebra and Logic, 2012, 51:2, 185–191

Bibliographic databases:

UDC: 512.57
Received: 15.05.2009
Revised: 16.12.2011

Citation: A. G. Pinus, “Semilattices of definable subalgebras. II”, Algebra Logika, 51:2 (2012), 276–284; Algebra and Logic, 51:2 (2012), 185–191

Citation in format AMSBIB
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