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...

the type of the applications for which internet is being used has changed over the years. multimedia applications, real-time applications and game playing require quality of service. ieee has proposed ieee 802.11e, a quality of service extension to the wireless lan standard ieee 802.11. in this paper service differentiation ability of 802.11e is evaluated. identical traffic is considered for al...

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...

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.

Figure 3(a) shows a temperature dependence ofthe fiber output and monitor current for one of the fabricated 50 samples of the plastic module. The fiber output was 0.2 mW in the full operating temperature range from -40-85°C. The monitor current was >lo0 (*.A at 0.2 mW fiber output and the trackingwidth of < + -20% was obtained in the full temperature range. The rise and fall time ofthe transmit...