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Fuzzy n-fold integral filters in BL-algebras

Rajab Ali BorzooeiAkbar Paad — 2013

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of fuzzy n-fold integral filter in BL-algebras and we state and prove several properties of fuzzy n-fold integral filters. Using a level subset of a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-fold integral filters. Also, we prove that the homomorphic image and preimage of fuzzy n-fold integral filters are also fuzzy n-fold integral filters. Finally, we study the relationship among fuzzy n-fold obstinate filters, fuzzy n-fold integral filters...

Module Structure on Effect Algebras

Simin Saidi GoraghaniRajab Ali Borzooei — 2020

Bulletin of the Section of Logic

In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. Finally, we introduce some topologies on effect modules.  

On ideal theory of hoops

Mona Aaly KologaniRajab Ali Borzooei — 2020

Mathematica Bohemica

In this paper, we define and characterize the notions of (implicative, maximal, prime) ideals in hoops. Then we investigate the relation between them and prove that every maximal implicative ideal of a -hoop with double negation property is a prime one. Also, we define a congruence relation on hoops by ideals and study the quotient that is made by it. This notion helps us to show that an ideal is maximal if and only if the quotient hoop is a simple MV-algebra. Also, we investigate the relationship...

PC-lattices: A Class of Bounded BCK-algebras

Sadegh Khosravi ShoarRajab Ali BorzooeiR. MoradianAtefe Radfar — 2018

Bulletin of the Section of Logic

In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition (S) and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being a new class of BCK-lattices. Specially, we prove that any Boolean lattice is a PC-lattice and we show that if X is a PC-lattice with condition S, then X is an involutory BCK-algebra if and only if X is a commutative BCK-algebra. Finally, we prove that any PC-lattice with condition...

Positive Implicative Soju Ideals in BCK-Algebras

Xiao Long XinRajab Ali BorzooeiYoung Bae Jun — 2019

Bulletin of the Section of Logic

The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.

On pseudo BE-algebras

Rajab Ali BorzooeiArsham Borumand SaeidAkbar RezaeiAkefe RadfarReza Ameri — 2013

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.

Soju Filters in Hoop Algebras

Rajab Ali BorzooeiGholam Reza RezaeiMona Aaly KologhaniYoung Bae Jun — 2021

Bulletin of the Section of Logic

The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.

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