Creator: Jakubík, Ján / Language: English / Subject: internal direct factor and lattice

Start Over Creator Jakubík, Ján Language English Subject internal direct factor Subject lattice

Creator:: Jakubík, Ján
Format:: bez média and svazek
Type:: model:article and TEXT
Subject:: bounded commutative residuated $\ell$-monoid, lattice, direct product decomposition, and internal direct factor
Language:: English
Description:: The notion of bounded commutative residuated $\ell $-monoid ($BCR$ $\ell $-monoid, in short) generalizes both the notions of $MV$-algebra and of $BL$-algebra. Let $\c A$ be a $BCR$ $\ell $-monoid; we denote by $\ell (\c A)$ the underlying lattice of $\c A$. In the present paper we show that each direct product decomposition of $\ell (\c A)$ determines a direct product decomposition of $\c A$. This yields that any two direct product decompositions of $\c A$ have isomorphic refinements. We consider also the relations between direct product decompositions of $\c A$ and states on $\c A$.
Rights:: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

Creator:: Jakubík, Ján
Format:: bez média and svazek
Type:: model:article and TEXT
Subject:: lattice, $\mathcal L^*$-variety, center, and internal direct factor
Language:: English
Description:: Freytes proved a theorem of Cantor-Bernstein type for algbras; he applied certain sequences of central elements of bounded lattices. The aim of the present paper is to extend the mentioned result to the case when the lattices under consideration need not be bounded; instead of sequences of central elements we deal with sequences of internal direct factors of lattices.
Rights:: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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