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Strict triangular norms and perfect MV-algebras

In: Tatra Mountains Mathematical Publications, vol. 16, no. 1
Lawrence Peter Belluce - Antonio Di Nola - Salvatore Sessa
Detaily:
Rok, strany: 1999, 1 - 9
O článku:
Abelian $ell$-groups and perfect MV-algebras are categorically equivalent via the functor $ riangle$ of Di Nola and Lettieri [A. Di Nola, A. Lettieri: Perfect MV-algebras are categorically equivalent to Abelian $ell$-groups, Studia Logica, 53, (1994), 417–432.] Thus the perfect MV-algebra $ riangle(Bbb R)$ corresponds to the classical $ell$-group $Bbb R$ of the reals. Given a strict triangular conorm $s: [0, 1]2 o[0,1]$, we build a perfect MV-algebra $A=(A, oplus, ·, *, 0A, 1A)$ such that $(Rad A oplus, 0A)$ and $([0,1), s, 0)$ are isomorphic Abelian ordered monoids. Further, we prove that $A$ is isomorphic to $ riangle(Bbb R)$ and a representation theorem for MV-algebras of functions of $ riangle(Bbb R)X$ type, $X$ being any nonempty set, is also given.
Ako citovať:
ISO 690:
Belluce, L., Di Nola, A., Sessa, S. 1999. Strict triangular norms and perfect MV-algebras. In Tatra Mountains Mathematical Publications, vol. 16, no.1, pp. 1-9. 1210-3195.

APA:
Belluce, L., Di Nola, A., Sessa, S. (1999). Strict triangular norms and perfect MV-algebras. Tatra Mountains Mathematical Publications, 16(1), 1-9. 1210-3195.