Prime, weakly prime and almost prime elements in multiplication lattice modules

Abstract

Abstract:In this paper, we study multiplication lattice modules. We establish a new multiplication over elements of a multiplication lattice module. With this multiplication, we characterize idempotent element, prime element, weakly prime element and almost prime element in multiplication lattice modules.

On gw-Prime Submodules

“…In [3], Hani A. Khashan and Ece Yetkin Celikel introduced a new type of weakly prime submodules which they called weakly 𝑆 −prime submodules and gave many properties and characterizations of them in multiplication modules. In [4] Emel Aslankarayigit Ugurlu proved some results concerning Sprime and S-weakly prime submodules. In [5] submodules and they studied the relation of this type of weakly prime submodules with valuation modules.…”