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...

Let L be a complete lattice. We introduce and characterize the prime L-submodules of a unitary module over a commutative ring with identity. Finally, we investigate the Zariski topology on the prime L-Spectrum of a unitary module, consisting of the collection of all prime L-submodules, and prove that for L-top modules the Zariski topology on L-Spec(M) exists. © 2007 Elsevier B.V. All rights res...

In this paper, we deal with arbitrarily shaped rectilinear module placement using the transitive closure graph (TCG) representation. The geometric meanings of modules are transparent to TCG as well as its induced operations, which makes TCG an ideal representation for floorplanning/placement with arbitrary rectilinear modules. We first partition a rectilinear module into a set of submodules and...