Functorial Representation Theorems for MVΔ Algebras with Additional Operators
✍ Scribed by Franco Montagna
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 203 KB
- Volume
- 238
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We prove functorial representation theorems for MV algebras, and for varieties ⌬ obtained from MV algebras by the adding of additional operators corresponding ⌬ w x to natural operations in the real interval 0, 1 , namely PMV algebras, obtained by ⌬ the adding of product, and Ł ⌸ algebras, obtained by the adding of product and of its residuum. Our first result is that the category of MV algebras is equivalent to ⌬ that of lattice ordered abelian groups with strong unit and with some kind of characteristic function. Our second result is that the category of PMV algebras is ⌬ equivalent to a category of commutative f-rings with strong unit, again with a Ž . suitable characteristic function, whose members modulo a forgetful functor are isomorphic to subdirect products of linearly ordered domains of integrity. Our Ž . third result in our opinion, the most interesting is that the category of Ł ⌸ algebras is equivalent to a category whose members are regular commutative f-rings with unit, equipped with an ideal with suitable properties.