Weakly Prime Elements in Lattice Modules
نویسنده
چکیده
As a generalization of the notion of prime element and semiprime element, we introduce the notion of weakly prime element and weakly semiprime element in lattice modules. Some characterization of weakly prime and weakly semiprime elements are obtained. Throughout this paper, L will be a lattice domain.
منابع مشابه
Prime elements in partially ordered groupoids applied to modules and Hopf algebra actions.∗
Primeness on modules can be defined by prime elements in a suitable partially ordered groupoid. Using a product on the lattice of submodules L(M) of a module M defined in [3] we revise the concept of prime modules in this sense. Those modules M for which L(M) has no nilpotent elements have been studied by Jirasko and they coincide with Zelmanowitz’ “weakly compressible” modules. In particular w...
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