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Abstract  
 The concept of right (left) quotient (or residual) of an ideal h by an ideal v of an L-subring m of a ring R is introduced. The right (left) quotients are shown to be ideals of m. It is proved that the right quotient [h:r v] of an ideal of h by an ideal v of an L-subring m is the largest ideal of m such that [h:r v]v ?h. Most of the results pertaining to the notion of quotients (or residual) of an ideal of ordinary rings are extended to L-ideal theory of L-subrings