we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

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...

in addition to the multimedia content repository, the module assumes the existence of a domain knowledge base (KB) described by a domain ontology, and the availability of annotations of the content by KB entities. one of the fundamental novel features provided by the module is a ranking algorithm integrating the classic iR view of the notion of relevance and approximate search results, with the...

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

membrane distillation has the potential to concentrate solutions to their saturation level, thus offering the possibility to recover valuable salts from the solutions. the process performance and stability, however, is strongly dependent upon the features of membranes applied. in addition, several other parameters, membrane thickness and thermal conductivity significantly affect the process per...

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

We continue the study of the fundamental series of generalized Harish-Chandra modules initiated in [PZ2]. Generalized Harish-Chandra modules are (g, k)-modules of finite type where g is a semisimple Lie algebra and k ⊂ g is a reductive in g subalgebra. A first result of the present paper is that a fundamental series module is a g-module of finite length. We then define the notions of strongly a...