We consider transformations preserving certain linear structure in Grassmannians and give some generalization of the Fundamental Theorem of Projective Geometry and the Chow Theorem [Ch]. It will be exploited to study linear (k, n − k)-involutions, 1 < k < n − 1. The analogy of the J. Dieudonné and C. E. Rickart result will be obtained.

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these d...

We study the transfer of (dual) relative CS-Rickart properties via functors between abelian categories. consider fully faithful as well adjoint pairs functors. give several applications to Grothendieck categories and, in particular, (graded) module and comodule

5. L. K. Hua, A note on the total matrix ring over a non-commutative field, Annales de la Société Polonaise de Mathématique vol. 25 (1952) pp. 188-198. 6. N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 479-502. 7. F. Kasch, Invariante Untermoduln des Endomorphismenrings eines Vektorraums, Archiv der Mathematik vol. 4 (1953) pp. 182-190. ...