This paper is dealed with a special local ring A and modules over A. Some properties of modules, that are constructed over the real plural algebra, are investigated. Moreover a module is constructed over the linear algebra of matrix Mmm(R) and one of its basis is found.

Let (O, E, U, V) be the coordination quadruple of the projective Klingenberg plane (PK-plane) coordinated with dual quaternion ring Q(ε)where Q is any quaternion ring over a field. In this paper, we define addition and multiplication of points on the line OU = [0, 1, 0] 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. MSC: 51C05; 51N35; 14A22; 16L30

Öz Bu makalede, girdileri bir F cisminden alınan mm  boyutlu özel bir matris cebiri çalışılmıştır. Bu cebir üzerinde tanımlanan bir ek (adjoint) alma dönüşümü (bir matrisin eki), bir norm form (bir matrisin determinantı) ve bir iz form (bir matrisin izi) yardımıyla bu cebir ile ilgili bazı cebirsel özellikler elde edildi. Ayrıca, bu cebirin. m dereceden bir cebir yapısına sahip olduğu gösterildi. Bu sonuç sayesinde kübik cebir tanımı. m dereceden cebir tanımına genişletildi.

In the present study, an (n+1)-dimensional module over the local ringK = Mmm(R) is constructed. Further, an n-dimensional projective coordinate space over this module is constructed with the help of equivalence classes. The points and lines of this space are determined and the points are classified. Finally, for a 3-dimensional projective coordinate space, the incidence matrix for a line that goes through the given points and also all points of a line given with the incidence matrix are found by the use of Maple commands.

No abstract