Characterizations of projective andk-projective semimodules

CHARACTERIZATIONS OF PROJECTIVE AND k-PROJECTIVE SEMIMODULES

On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective

Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...

Cohomological Characterizations of Projective Spaces and Hyperquadrics

Projective spaces and hyperquadrics are the simplest projective algebraic varieties, and they can be characterized in many ways. The aim of this paper is to provide a new characterization of them in terms of positivity properties of the tangent bundle (Theorem 1.1). The first result in this direction was Mori’s proof of the Hartshorne conjecture in [Mor79] (see also Siu and Yau [SY80]), that ch...

Characterizations of Finite Projective and Affine Spaces

THEOREM 1. A finite incidence structure is isomorphic to the design of points and hyperplanes of a finite projective or affine space of dimension greater than or equal to 4 if and only if there are positive integers v, k, and y, with ju > 1 and (/A — l)(v — k) 7* (k — ju) such that the following assumptions hold. (I) Every block is on k points, and every two intersecting blocks are on p. common...

K-FLAT PROJECTIVE FUZZY QUANTALES

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.