BL-algebras are the Lindembaum algebras of the propositional calculus coming from the continuous triangular norms and their residua in the real unit interval. Any BL-algebra is a subdirect product of local (linear)BLalgebras. A local BL-algebra is either locally finite (and hence an MValgebra) or perfect or peculiar. Here we study extensively perfect BLalgebras characterizing, with a finite sch...

In this paper, the author examines the notion of n-fold fantastic and fuzzy n-fold fantastic filters in BLalgebras. Several characterizations of fuzzy n-fold fantastic filters are given. The author shows that every n-fold (fuzzy n-fold) fantastic filter is a filter (fuzzy filter), but the converse is not true. Using a level set of a fuzzy set in a BL-algebra, the author gives a characterization...

The concepts of (∈,∈ ∨ q)-fuzzy (implicative, positive implicative and fantastic) filters of BL-algebras are introduced and some related properties are investigated. Some characterizations of these generalized fuzzy filters are derived. In particular, we describe the relationships among ordinary fuzzy (implicative, positive implicative and fantastic) filters, (∈,∈∨q)-fuzzy (implicative, positiv...

In recent years much attention has been given to a certain spectral sequence relating motivic cohomology to algebraic K-theory [Be, BL, FS, V3]. This spectral sequence takes on the form H(X,Z(− q 2 )) ⇒ K(X), where the H(X ;Z(t)) are the bi-graded motivic cohomology groups, and K(X) denotes the algebraic K-theory of X . It is useful in our context to use topologists’ notation and write K(X) for...

Multiple-valued logics are non-classical logics. They are similar to classical logic because they accept the principle of truth-functionality, namely, the truth of a compound sentence is determined by the truth values of its component sentences (and so remains unaffected when one of its component sentences is replaced by another sentence with the same truth value). But they differ from classica...

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...

In this paper we study the prime ideals space of a BL-algebra, proved that the prime ideals space being a 0 T-space and also a stone space. Furthermore, we study the properties of the prime ideals space.

In this paper, the authors study the notion of n-fold implicative and fuzzy n-fold implicative filters, which correspond to various sets of provable formulaes, in BL-algebras. Several characterizations of fuzzy n-fold implicative filters are given and the authors analyse some relationships with various n-fold and fuzzy n-fold filters in BL-algebras, while constructing some algorithms for studyi...

The aim of this paper is to introduce the notion of (∈,∈∨ q)-fuzzy (implicative, MV and G-) filters of pseudo-BL algebras and to investigate some of their related properties. Some characterization theorems of these generalized fuzzy (implicative) filters are derived. The relationship among these generalized fuzzy filters of pseudo-BL algebras is considered. It is proved that an (∈,∈ ∨q)-fuzzy f...

The aim of the present paper is to define the localization BL-algebra of a BL-algebra A with respect to a topology F on A. In the last part of the paper is proved that the maximal BL-algebra of quotients (defined in [5]) and the BLalgebra of fractions relative to a ∧-closed system (defined in [4]) are BL-algebras of localization. A remarkable construction in ring theory is the localization ring...