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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.

Quantum B-algebras

Wolfgang Rump (2013)

Open Mathematics

The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated posets,...

Quantum logics and bivariable functions

Eva Drobná, Oľga Nánásiová, Ľubica Valášková (2010)

Kybernetika

New approach to characterization of orthomodular lattices by means of special types of bivariable functions G is suggested. Under special marginal conditions a bivariable function G can operate as, for example, infimum measure, supremum measure or symmetric difference measure for two elements of an orthomodular lattice.

Quasi-implication algebras

Ivan Chajda, Kamil Dušek (2002)

Discussiones Mathematicae - General Algebra and Applications

A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having non-involutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutual correspondence between this algebra and a quasi-implication algebra is shown.

Quasi-modal algebras

Sergio A. Celani (2001)

Mathematica Bohemica

In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.

Quotient hyper pseudo BCK-algebras

Habib Harizavi, Tayebeh Koochakpoor, Rajab Ali Boorzoei (2013)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we first investigate some properties of the hyper pseudo BCK-algebras. Then we define the concepts of strong and reflexive hyper pseudo BCK-ideals and establish some relationships among them and the other types of hyper pseudo BCK-ideals. Also, we introduce the notion of regular congruence relation on hyper pseudo BCK-algebras and investigate some related properties. By using this relation, we construct the quotient hyper pseudo BCK-algebra and give some related results.

R 0 -algebras and weak dually residuated lattice ordered semigroups

Liu Lianzhen, Li Kaitai (2006)

Czechoslovak Mathematical Journal

We introduce the notion of weak dually residuated lattice ordered semigroups (WDRL-semigroups) and investigate the relation between R 0 -algebras and WDRL-semigroups. We prove that the category of R 0 -algebras is equivalent to the category of some bounded WDRL-semigroups. Moreover, the connection between WDRL-semigroups and DRL-semigroups is studied.

Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras

Akbar Paad (2016)

Discussiones Mathematicae General Algebra and Applications

In this paper, we study relationships between among (fuzzy) Boolean ideals, (fuzzy) Gödel ideals, (fuzzy) implicative filters and (fuzzy) Boolean filters in BL-algebras. In [9], there is an example which shows that a Gödel ideal may not be a Boolean ideal, we show this example is not true and in the following we prove that the notions of (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras coincide.

Relative co-annihilators in lattice equality algebras

Sogol Niazian, Mona Aaly Kologani, Rajab Ali Borzooei (2024)

Mathematica Bohemica

We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among ∨ -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra 𝔼 and 𝔽 a filter of 𝔼 , we define the set of all 𝔽 -involutive filters of 𝔼 and show that by defining some operations on it, it makes a BL-algebra.

Currently displaying 481 – 500 of 710