Andrzej Walendziak (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is proved that every branchwise commutative pseudo-BCH algebra is a pseudo-BCI algebra.
Magdalena Wojciechowska-Rysiawa (2010)
Discussiones Mathematicae - General Algebra and Applications
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Pseudo BL-algebras are a noncommutative extention of BL-algebras. In this paper we study good pseudo BL-algebras and consider some classes of these algebras.
Grzegorz Dymek (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.
Akbar Rezaei, Arsham Borumand Saeid, Andrzej Walendziak (2017)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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The notions of a dual pseudo-Q algebra and a dual pseudo-QC algebra are introduced. The properties and characterizations of them are investigated. Conditions for a dual pseudo-Q algebra to be a dual pseudo-QC algebra are given. Commutative dual pseudo-QC algebras are considered. The interrelationships between dual pseudo-Q/QC algebras and other pseudo algebras are visualized in a diagram.
Grzegorz Dymek (2015)
Annales UMCS, Mathematica
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The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.
Walendziak, Andrzej (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Andrzej Walendziak (2015)
Discussiones Mathematicae - General Algebra and Applications
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The notion of pseudo-BCH-algebras is introduced, and some of their properties are investigated. Conditions for a pseudo-BCH-algebra to be a pseudo-BCI-algebra are given. Ideals and minimal elements in pseudo-BCH-algebras are considered.
Besnard, F. (2001)
Mathematical Physics Electronic Journal [electronic only]
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Habib Harizavi, Tayebeh Koochakpoor, Rajab Ali Boorzoei (2013)
Discussiones Mathematicae - General Algebra and Applications
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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. ...
Ivan Chajda, Helmut Länger (2016)
Mathematica Bohemica
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In Chajda's paper (2014), to an arbitrary BCI-algebra the author assigned an ordered structure with one binary operation which possesses certain antitone mappings. In the present paper, we show that a similar construction can be done also for pseudo-BCI-algebras, but the resulting structure should have two binary operations and a set of couples of antitone mappings which are in a certain sense mutually inverse. The motivation for this approach is the well-known fact that every commutative...
Doh, Myung Im, Kang, Min Su (2011)
International Journal of Mathematics and Mathematical Sciences
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Grzegorz Dymek (2015)
Discussiones Mathematicae - General Algebra and Applications
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The notions of a period of an element of a pseudo-BCI-algebra and a periodic pseudo-BCI-algebra are defined. Some of their properties and characterizations are given.
Young Bae Jun, Hee Sik Kim, J. Neggers (2006)
Matematički Vesnik
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Rajab Ali Borzooei, Arsham Borumand Saeid, Akbar Rezaei, Akefe Radfar, Reza Ameri (2013)
Discussiones Mathematicae - General Algebra and Applications
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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. ...
Ivan Chajda (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members.