Yazar "Icen, Ilhan" seçeneğine göre listele

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    Actions of R-module groupoids
    (Univ Nis, Fac Sci Math, 2023) Ozcan, Abdullah Fatih; Icen, Ilhan
    Let R be a ring, 1R be the identity of ring R and N be an R-module on R. In this work, we are going to give a new definition that it is called an action of R-module groupoids. First, we are going to give the definition of the action of the R-module groupoids on the R-module N. Then we obtained a new category RMGpdOp(Omega) of actions of Omega on R-modules. We also find that there is a groupoid Omega (sic) N on N. Omega (sic) N is called action R-module groupoid. Finally, we prove that the category RMGpdOp(Omega) of actions of R-module groupoids is equivalent to RMGpdCov(Omega) of coverings of R-module groupoids.
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    Coverings of structured Lie groupoids
    (Hacettepe Univ, Fac Sci, 2018) Gursoy, M. Habil; Icen, Ilhan
    In this work, we present some results related to coverings of structured Lie groupoids. Firstly, we obtain a covering Lie group-groupoid and a covering morphism of Lie group-groupoids from a given Lie group-groupoid by the notion of action. Secondly, we show how the Lie group structure of a Lie group-groupoid is lifted to a covering Lie groupoid. Then, we give similar results for Lie ring-groupoid which is also a structured Lie groupoid.
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    Generalized crossed modules and group-groupoids
    (Tubitak Scientific & Technological Research Council Turkey, 2017) Gursoy, Mustafa Habil; Aslan, Hatice; Icen, Ilhan
    In this present work, we present the concept of a crossed module over generalized groups and we call it a generalized crossed module. We also define a generalized group-groupoid. Furthermore, we show that the category of generalized crossed modules is equivalent to that of generalized group-groupoids whose object sets are abelian generalized group.
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    Lie Rough Groups
    (Univ Nis, Fac Sci Math, 2018) Oguz, Gulay; Icen, Ilhan; Gursoy, M. Habil
    This paper introduces the definition of a Lie rough group as a natural development of the concepts of a smooth manifold and a rough group on an approximation space. Furthermore, the properties of Lie rough groups are discussed. It is shown that every Lie rough group is a topological rough group, and that the product of two Lie rough groups is again a Lie rough group. We define the concepts of Lie rough subgroups and Lie rough normal subgroups. Finally, our aim is to give an example by using definition of Lie rough homomorphism sets G and H.
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    Modeling the Relations between Countries with Graph Theory and Possible Separations
    (Turgut Ozal Univ, 2012) Sulu, Mucahit; Karci, Ali; Icen, Ilhan
    The aim of this study is to examine present-day countries' economic, political and religious relationships, and also to examine conflicts between these countries by transferring the conflicts to a graph. With the help of the eigenvalues and eigenvectors of the matrix obtained from the graph, the study aims to identify where the graph could be divided. By making use of this division, which is a result of weak ties between countries, the study aims to find out which weak ties should be analyzed in order not for a division to take place.
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    A Soft Approach to Ring-Groupoids
    (E D P Sciences, 2018) Oguz, Gulay; Gursoy, M. Habil; Icen, Ilhan
    This study introduces a soft approach to the concept of ring-groupoid which is the one of the structured groupoids. Some properties and characterizations of soft ring-groupoids are established. Also, the category of soft ring-groupoids constructed by the homomorphism between two soft ring-groupoids is presented.
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    Soft Sets and Soft Topology on Nearness Approximation Spaces
    (Univ Nis, Fac Sci Math, 2017) Tasbozan, Hatice; Icen, Ilhan; Bagirmaz, Nurettin; Ozcan, Abdullah Fatih
    Near set theory presents a fundamental basis for observation, comparison and classification of perceptual granules. Soft set theory is proposed as a general framework to model vagueness. The purpose of this paper is to combine these two theories in what are known near soft sets in defining near soft topology based on a nearness approximation space.