Pseudo MV-algebras and lexicographic product
Copyright policy )Pseudo MV-algebras and lexicographic product
We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group that is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebras and strong $(H,u)$-perfect pseudo MV-algebras, the latter ones will have a representation by a lexicographic product. Fixing a unital $\ell$-group $(H,u)$, the category of strong $(H,u)$-perfect pseudo MV-algebras is categorically equivalent to the category of $\ell$-groups.
arXiv admin note: text overlap with arXiv:1304.0743
- Slovak Academy of Sciences Slovakia
MV-algebras, strong unit, ideal, retractive ideal, Mathematics - Rings and Algebras, pseudo MV-algebra, strongly \((H, u)\)-perfect pseudo MV-algebra, 03G20, Rings and Algebras (math.RA), \((H, u)\)-perfect pseudo MV-algebra, symmetric pseudo MV-algebra, lexicographic pseudo MV-algebra, FOS: Mathematics, Ordered groups, lexicographic product, \(\ell\)-group
MV-algebras, strong unit, ideal, retractive ideal, Mathematics - Rings and Algebras, pseudo MV-algebra, strongly \((H, u)\)-perfect pseudo MV-algebra, 03G20, Rings and Algebras (math.RA), \((H, u)\)-perfect pseudo MV-algebra, symmetric pseudo MV-algebra, lexicographic pseudo MV-algebra, FOS: Mathematics, Ordered groups, lexicographic product, \(\ell\)-group
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