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Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

Dana Piciu (2004)

Open Mathematics

The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem...

Pure filters and stable topology on BL-algebras

Esfandiar Eslami, Farhad Kh. Haghani (2009)

Kybernetika

In this paper we introduce stable topology and F -topology on the set of all prime filters of a BL-algebra A and show that the set of all prime filters of A , namely Spec( A ) with the stable topology is a compact space but not T 0 . Then by means of stable topology, we define and study pure filters of a BL-algebra A and obtain a one to one correspondence between pure filters of A and closed subsets of Max( A ), the set of all maximal filters of A , as a subspace of Spec( A ). We also show that for any filter...

Putting together Lukasiewicz and product logics.

Francesc Esteva, Lluis Godo (1999)

Mathware and Soft Computing

In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.

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