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Corpus ID: 14324884

DIRECT DECOMPOSITIONS OF BASIC ALGEBRAS AND THEIR IDEMPOTENT MODIFICATIONS

@inproceedings{Chajda2009DIRECTDO,
title={DIRECT DECOMPOSITIONS OF BASIC ALGEBRAS AND THEIR IDEMPOTENT MODIFICATIONS},
author={Ivan Chajda},
year={2009}
}

We get a necessary and sufficient condition under which a given basic algebraA is isomorphic to a direct product of non-trivial basic algebras A1,A2 which are in fact interval subalgebras of A. Further, we prove that the idempotent modification of A is directly indecomposable whenever A has at least one element which is not boolean.

The notion of idempotent modification of an algebra was introduced by Ježek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that… Expand

It is proved that the axiom system of basic algebras as given in Chajda and Emanovský is not independent and the remaining axioms are shown to be independent.Expand

Direct decomposition of basic algebras and their idempotent modifications

Acta Univ . M . Belii

2009

Chajda) Department of Algebra and Geometry, Palack´Palack´y University Olomouc, Třída 17. listopadu 12, 771 46 Olomouc, Czech Republic E-mail address, I. Chajda: chajda@inf.upol

Chajda) Department of Algebra and Geometry, Palack´Palack´y University Olomouc, Třída 17. listopadu 12, 771 46 Olomouc, Czech Republic E-mail address, I. Chajda: chajda@inf.upol

A note on idempotent modification of groups, Czechoslovak Math