CLASSICAL PRIME an‎d 2-ABSORBING L-SUBMODULES

LetLbeacompletelattice.LetRbeacommutativering,ManR-moduleandνanL-submoduleofM.νiscalledaclassicalprimeL-submoduleofMifforanyL-fuzzypointsar,bs∈LRandxt∈LM(a,b∈R,x∈Mandr,s,t∈L),arbsxt∈νimpliesthateitherarxt∈νorbsxt∈ν.AssumethatνisanL-submoduleofmmu∈L(M).Wesaythatνisa2-absorbingL-submoduleofμifforanyL-fuzzypointsar,bs∈LRandxt∈LM(a,b∈R,x∈Mandr,s,t∈L),arbsxt∈νimpliesthatarbsμ⊆νorarxt∈νorbsxt∈ν.InthiscaseeveryprimeL-submoduleofMisaclassicalprimeL-submodule,andeveryclassicalprimeL-submoduleisa2-absorbingL-submodule.InthispaperwegivesomebasicresultsconcerningtheseclassesofL-submodules.FinallywetopologizeL−Cl.Spec(M),thesetofallclassicalprimeL-submodulesofM,withZariskitopology.