Classical Prime and 2-Absorbing L-Submodules

Let l be a complete lattice. let r be a commutative ring, m an r-module and ν an l-submodule of m. ν is called a classical prime l-submodule of m if for any l-fuzzy points ar, bs ∈ lr and xt ∈ lm (a, b ∈ r, x ∈ m and r, s, t ∈ l), arbsxt ∈ ν implies that either arxt ∈ ν or bsxt ∈ ν. assume that ν is an l-submodule of mmu ∈ l(m). we say that ν is a 2-absorbing l-submodule of µ if for any l-fuzzy points ar, bs ∈ lr and xt ∈ lm (a, b ∈ r, x ∈ m and r, s, t ∈ l), arbsxt ∈ ν implies that arbsµ ⊆ ν or arxt ∈ ν or bsxt ∈ ν. in this case every prime l-submodule of m is a classical prime l-submodule, and every classical prime l-submodule is a 2-absorbing l-submodule. in this paper we give some basic results concerning these classes of l-submodules. finally we topologize l−cl.spec(m), the set of all classical prime l-submodules of m, with zariski topology.