In this paper we introduce the notions of G∗L-module and G∗L-module whichare two proper generalizations of δ-lifting modules. We give some characteriza tions and properties of these modules. We show that a G∗L-module decomposesinto a semisimple submodule M1 and a submodule M2 of M such that every non-zero submodule of M2 contains a non-zero δ-cosingular submodule.

This paper describes a Web-based Test, Examination and Assessment system that can be used via the Internet. It is therefore suitable for both local and remote examination preparation as well as examination within a lab course (entry test). This solution is also intended for the use in lectures dealing with the design of complex digital control systems within the newly created European Master De...

A Hopf module is an A-module for an algebra A as well as a C-comodule for a coalgebra C, satisfying a suitable compatibility condition between the module and comodule structures. To formulate the compatibility condition one needs some kind of interaction between A and C. The most classical case arises when A = C =: H is a bialgebra. Many subsequent variants of this were unified independently by...

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

The ultimate purpose of this part is to explain the definition of models for the rational homotopy of spaces. In our constructions, we use the classical Sullivan model, defined in terms of unitary commutative cochain dg-algebras, and a cosimplicial version of this model, involving cosimplicial algebra structures. The purpose of this preliminary chapter is to provide a survey of constructions on...

Our dual notions “locally injective” and “locally projective” modules in Mod-R are good tools to study the relations between the singular, respectively cosingular, submodule of Hom R(M, W ) and the total Tot (M, W ). These notions have further interesting properties.

Today, great observatories around the world, devote a substantial amount of observing time to sky surveys. The resulted images are inputs of source finder modules. These modules search for the target objects and provide us with source catalogues. We sought to quantify the ability of detection tools in recovering faint galaxies regularly encountered in deep surveys. Our approach was based on com...

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...