A (continuous) t-norm is called equationally definable when the corresponding standard BL-algebra [0, 1]∗ defined by ∗ and its residuum is the only (up to isomorphism) standard BL-algebra that generates the same variety Var([0, 1]∗). In this chapter we check that a continuous t-norm ∗ is equationally definable if and only if the t-norm is a finite ordinal sum of copies of the three basic contin...

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters. Mathematics Subject Cla...

In this paper, the notions of tense operators and filters in \(BL\)-algebras are introduced several characterizations them obtained. Also, relation among \(BL\)-algebras, \(MV\)-algebras Boolean algebras investigated. Moreover, it is shown that set all a \(BL\)-algebra complete sublattice \(F(L)\) \(L\). maximal simple between studied. Finally, congruence relations strict an one-to-one correspo...

We prove that RS-BL-algebras are MV-algebras.

The notion of a state is an analogue of a probability measure and was first introduced by Kôpka and Chovanec for MV-algebras and by Riec̆an for BLalgebras. The states have also been studied for different types of non-commutative fuzzy structures such as pseudo-MV algebras, pseudo-BL algebras, bounded R`monoids, residuated lattices and pseudo-BCK semilattices. In this paper we investigate the sta...

Although the notions of a BL-algebra and of an effect algebra arose in rather different contextes, both types of algebras have certain structural properties in common. To clarify their mutual relation, we introduce weak effect algebras, which generalize effect algebras in that the order is no longer necessarily determined by the partial addition. A subclass of the weak effect algebras is shown ...

In this paper, we present a general definition of the notion Noetherian and Artinian BL-algebra more comprehensive insight at chain conditions in BL-algebras. We derive some theorems which generalize existence results. give an axiomatic approach to being Artinian, is also applicable other algebraic structures. use theoretical define arithmetic that possible for devices. study, only focus

This material is studying MV-algebras and BL-algebras in terms of applicability in Boole algebra. Boole algebras are expanded use in fuzzy logic.

An element u of a norm-unital Banach algebra A is said to be unitary if u is invertible in A and satisfies ‖u‖ = ‖u−1‖ = 1. The norm-unital Banach algebra A is called unitary if the convex hull of the set of its unitary elements is norm-dense in the closed unit ball of A . If X is a complex Hilbert space, then the algebra BL(X) of all bounded linear operators on X is unitary by the Russo–Dye th...

A generalized BL-algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities x ∧ y = ((x ∧ y)/y)y = y(y\(x∧ y)). It is shown that all finite GBL-algebras are commutative, hence they can be constructed by iterating ordinal sums and direct products of Wajsberg hoops. We also observe that the idempotents in a GBL-algebra form a subalgebra of elements that commute with ...