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Start Over Coverage 243-252

2. On idempotent modifications of $MV$-algebras

Creator:
Jakubík, Ján
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$MV$-algebra, idempotent modification, and subdirect reducibility
Language:
English
Description:
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an $MV$-algebra $\mathcal A$ we denote by $\mathcal A^{\prime }, A$ and $\ell (\mathcal A)$ the idempotent modification, the underlying set or the underlying lattice of $\mathcal A$, respectively. In the present paper we prove that if $\mathcal A$ is semisimple and $\ell (\mathcal A)$ is a chain, then $\mathcal A^{\prime }$ is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. The ${\scr Ar}$-free products of archimedean $l$-groups

Creator:
Ton, Dao-Rong
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math, weak subalgebra, and Archimedean groups
Language:
English
Description:
The objective of this paper is to give two descriptions of the $\scr A r$-free products of archimedean $\ell $-groups and to establish some properties for the $\scr A r$-free products. Specifically, it is proved that $\scr A r$-free products satisfy the weak subalgebra property.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public