Browsing by Author "Erdoǧan, Fatma Özen"
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Item A Class of Projective Coordinate Spaces Over Modules(Asian-European Journal of Mathematics, 2020-08) Akpınar, Atilla; Erdoǧan, Fatma Özen; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; https://orcid.org/0000-0002-7612-2448; AAG-8274-2021; ABB-9790-2020; 23026537500; 54402700700In this paper, we study a class of local rings that are not isomorphic to the class of two local rings we have been working on before. This class is also an isomorphism to a special matrix algebra. We construct a projective coordinate space over a module defined on this special algebra class. Specifically, in a 3-dimensional projective coordinate space, the incidence matrix for a line that combines the certain two points and also all points of a line given with the incidence matrix are found by the help of Maple programme. © 2020 World Scientific Publishing Company.Item On addition and multiplication of points in a certain class of projective Klingenberg planes(Springer, 2013-12) Çelik, Basri; Erdoǧan, Fatma Özen; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-7234-8063; AAE-2600-2019; AAG-8274-2021; 23026643900; 54402700700Let be the coordination quadruple of the projective Klingenberg plane (PK-plane) coordinated with dual quaternion ring , where Q is any quaternion ring over a field. In this paper, we define addition and multiplication of points on the line geometrically, also we give the algebraic correspondences of them. Finally, we carry over some well-known properties of ordinary addition and multiplication to our definition.Item On some geometric structures and local rings(Amer Inst Physics, 2011) Simos, T. E.; Erdoǧan, Fatma Özen; Çelik, Basri; Çiftçi, Süleyman; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-7234-8063; AAE-2600-2019; AAG-8274-2021; 54402700700; 23026643900; 26635052900In this paper, we investigate some combinatoric properties of the Projective Klingenberg planes coordinatized with a finite local ring R when the cardinality of set I of the non-unit elements of R is k. As a result we arrive at the result that the order of the projective plane underlying projective Klingenberg plane must be n k, which is the index of I in R when |R| = n. Although some of the results given here can be found in the literature [1], [3] and [4] we approach to them in a direct way and give alternative proofs.