Let R be a commutative ring with identity and M an R–module. If M is either locally cyclic projective or faithful multiplication then M is locally either zero or isomorphic to R. We investigate locally cyclic projective modules and the properties they have in common with faithful multiplication modules. Our main tool is the trace ideal. We see that the module structure of a locally cyclic proje...

The object of the present paper is to study the totally umbilical hypersurfaces of weakly projective symmetric spaces and it is shown that the totally umbilical hypersurfaces of weakly projective symmetric space is also a weakly projective symmetric space.

Planar shapes recognition is an important problem in computer vision and pattern recognition. We deal with planar shape contour views that differ by a general projective transformation. One method for solving such problem is to use projective invariants. In this work, we propose a projective and parameterization invariant generation framework based on the harmonic analysis theory. In fact, inva...

We investigate the structure of pure-syzygy modules in a pure-projective resolution of any right R-module over an associative ring R with an identity element. We show that a right R-module M is pure-projective if and only if there exists an integer n ≥ 0 and a pure-exact sequence 0 → M → Pn → · · · → P0 → M → 0 with pure-projective modules Pn, . . . , P0. As a consequence we get the following v...

A function projective synchronization is defined to synchronize two different systems up to a scaling function matrix f with different initial values. The function projective synchronization is more general than the complete synchronization, the generalized projective synchronization and the modified projective synchronization. The corresponding framework of synchronization is set up and used t...

In this paper, we investigate the evolution of curves of the projective plane according to a family of projective invariant intrinsic equations. This is motivated by previous work for the Euclidean 9, 10, 13] and the aane cases 19, 20, 3, 2] as well as by applications in the perception of two-dimensional shapes. We establish the evolution laws for the projective arclength and curvature. Among t...

Since Eilenberg and Moore [EM], the relative homological algebra, especially the Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The analogues for the basic notion, such as projective, injective, flat, and free modules, are respectively the Gorenstein projective, the Gorenstein injective, the Gorenstein flat, and the strongly Gorenstein projective modules. One c...

We will generalize the projective model structure in the category of unbounded complexes of modules over a commutative ring to the category of unbounded complexes of quasi-coherent sheaves over the projective line. Concretely we will define a locally projective model structure in the category of complexes of quasicoherent sheaves on the projective line. In this model structure the cofibrant obj...

The projective shape of a configuration consists of the information that is invariant under projective transformations. It encodes the information about an object reconstructable from uncalibrated camera views. The space of projective shapes of k points in RP is by definition the quotient space of k copies of RP modulo the action of the projective linear group PGLpdq. A detailed examination of ...