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In this paper, we show that D + D(ε) is a local ring under usual operations where D is a division ring. Also we construct aprojective Klingenberg plane overD + D(ε). [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

In the present study, an (n+1)-dimensional module over the local ring K = Mmm(R) is constructed. Further, an n- dimensional projective coordinate space over this module is constructed by 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. [ABSTRACT FROM AUTHOR]