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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.
Paolo Vitolo (2010)
Kybernetika
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An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.
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.
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.
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.
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.
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...
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. ...
Besnard, F. (2001)
Mathematical Physics Electronic Journal [electronic only]
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Doh, Myung Im, Kang, Min Su (2011)
International Journal of Mathematics and Mathematical Sciences
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Grzegorz Dymek (2011)
Discussiones Mathematicae - General Algebra and Applications
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The class of p-semisimple pseudo-BCI-algebras and the class of branchwise commutative pseudo-BCI-algebras are studied. It is proved that they form varieties. Some congruence properties of these varieties are displayed.