A Remark on Structure of Projective Klingenberg Spaces over a Certain Local Algebra

Abstract

This article is devoted to the projective Klingenberg spaces over a local ring, which is a linear algebra generated by one nilpotent element. In this case, subspaces of such Klingenberg spaces are described. The notion of the “degree of neighborhood” is introduced. Using this, we present the geometric description of subsets of points of a projective Klingenberg space whose arithmetical representatives need not belong to a free submodule.

Keywords

• projective Klingenberg space
• point
• hyperplane
• local ring
• plural algebra
• A-space
• A-subspace
• neighbor points