We prove functorial representation theorems for MVDelta algebras, and for varieties obtained from MVDelta algebras by the adding of additional operators corresponding to natural operations in the real interval [0, 1], namely PMVDelta algebras, obtained by the adding of product, and LII algebras, obtained by the adding of product and of its residuum. Our first result is that the category of MVDelta 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 PMVDelta algebras is equivalent to a category of commutative f-rings with strong unit, again with a suitable characteristic function, whose members (modulo a forgetful functor) are isomorphic to subdirect products of linearly ordered domains of integrity. Our third result (in our opinion, the most interesting) is that the category of LII algebras is equivalent to a category whose members are regular commutative f-rings with unit, equipped with an ideal with suitable properties. (C) 2001 Academic Press.

Montagna, F. (2001). Functorial representation theorems for MV-Delta algebras with additional operators. JOURNAL OF ALGEBRA, 238(1), 99-125 [10.1006/jabr.2000.8633].

Functorial representation theorems for MV-Delta algebras with additional operators

MONTAGNA, FRANCO
2001

Abstract

We prove functorial representation theorems for MVDelta algebras, and for varieties obtained from MVDelta algebras by the adding of additional operators corresponding to natural operations in the real interval [0, 1], namely PMVDelta algebras, obtained by the adding of product, and LII algebras, obtained by the adding of product and of its residuum. Our first result is that the category of MVDelta 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 PMVDelta algebras is equivalent to a category of commutative f-rings with strong unit, again with a suitable characteristic function, whose members (modulo a forgetful functor) are isomorphic to subdirect products of linearly ordered domains of integrity. Our third result (in our opinion, the most interesting) is that the category of LII algebras is equivalent to a category whose members are regular commutative f-rings with unit, equipped with an ideal with suitable properties. (C) 2001 Academic Press.
Montagna, F. (2001). Functorial representation theorems for MV-Delta algebras with additional operators. JOURNAL OF ALGEBRA, 238(1), 99-125 [10.1006/jabr.2000.8633].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/17178
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