Yazar "Davvaz, Bijan" seçeneğine göre listele

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    Cat1-polygroups and pullback cat1-polygroups
    (Iranian Mathematical Society, 2014) Davvaz, Bijan; Alp, Murat
    In this paper, we give the notions of crossed polymodule and cat1-polygroup as a generalization of Loday's definition. Then, we define the pullback cat1-polygroup and we obtain some results in this respect. Specially, we prove that by a pullback cat1- polygroup we can obtain a cat1-group. © 2014 Iranian Mathematical Society.
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    Crossed modules of hypergroups associated with generalized actions
    (HACETTEPE UNIV, FAC SCI, 2016) Alp, Murat; Davvaz, Bijan
    In this article, by using the notion of generalized action, we introduce the concept of crossed module of hypergroups, in the sense of Marty, and its related structures from the light of crossed polymodules. Hyper-groups in the sense of Marty are more different than polygroups since they have not identity element or inverse element in general. Examples of crossed modules of hypergroups are originally presented. These examples illustrate the structure and behavior of crossed modules of hypergroups. Moreover, we obtain a crossed module in the sense of Whitehead from a crossed module of hypergroups by applying the notion of fundamental relation.
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    CROSSED POLYMODULES AND FUNDAMENTAL RELATIONS
    (UNIV POLITEHNICA BUCHAREST, SCI BULL, 2015) Alp, Murat; Davvaz, Bijan
    In this paper, we introduce the notion of crossed polymodule of polygroups and we give some of its properties. Our results extend the classical results of crossed modules to crossed polymodules. One of the main tools in the study of polygroups is the fundamental relations. These relations connect polygroups to groups, and on the other hand, introduce new important classes. So, we consider a crossed polymodule and by using the concept of fundamental relation, we obtain a crossed module. Moreover, we give a crossed polymodule morphism between them.
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    Crossed polymodules and fundamental relations
    (Politechnica University of Bucharest, 2015) Alp, Murat; Davvaz, Bijan
    In this paper, we introduce the notion of crossed polymodule of poly-groups and we give some of its properties. Our results extend the classical results of crossed modules to crossed polymodules. One of the main tools in the study of polygroups is the fundamental relations. These relations connect polygroups to groups, and on the other hand, introduce new important classes. So, we consider a crossed polymodule and by using the concept of fundamental relation, we ob-tain a crossed module. Moreover, we give a crossed polymodule morphism between them.
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    Pullback and pushout crossed polymodules
    (INDIAN ACAD SCIENCES, 2015) Alp, Murat; Davvaz, Bijan
    In this paper, we introduce the concept of pullback and pushout crossed polymodules and we describe the construction of pullback and pushout crossed polymodules. In particular, by using the notion of fundamental relation, we obtain a crossed module from a pullback crossed polymodule.