The Fundamental Theorem of Projective Geometry for an Arbitrary Length Two Module

The fundamental theorem of projective geometry

We prove the fundamental theorem of projective geometry. In addition to the usual statement, we also prove a variant in the presence of a symplectic form.

The Fundamental Theorem of q-Clan Geometry

"Fundamental theorem" for two Loci.

THE CHANGE IN MEAN FITNESS FOR TWO LOCI UNDER SELECTION CAN BE DESCRIBED BY FOUR TERMS: (i) the variance of fitness, (ii) a weighted between-gamete covariance, (iii) a function of recombination, linkage disequilibrium and the slope of the surface of mean fitness on disequilibrium, and (iv) a function of these two parameters and the curvature of the surface. Independent derivations of this equat...

Extension of Krull's intersection theorem for fuzzy module

‎In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...

Fundamental Theorem of Geometry without the 1-to-1 Assumption

It is proved that any mapping of an n-dimensional affine space over a division ring D onto itself which maps every line into a line is semiaffine, if n ∈ {2, 3, . . . } and D 6= Z2. This result seems to be new even for the real affine spaces. Some further generalizations are also given. The paper is self-contained, modulo some basic terms and elementary facts concerning linear spaces and also –...