On inverse operations in the lattices of submodules

Abstract

In the lattice L(RM) of submodules of an arbitrary left R-module RM four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for α-product and ω-coproduct) are defined and studied. Some properties of left quotient with respect to α-product and right quotient with respect to ω-coproduct are shown, as well as their relations with the lattice operations in L(RM) (sum and intersection of submodules). The particular case RM = RR of the lattice L(RR) of left ideals of the ring R is specified.