1. Direct product decompositions of bounded commutative residuated $\ell$-monoids
- 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