Abstract
The concept of right (left) quotient (or residual) of an ideal η by an ideal ν of an L-subring µ of a ring R is introduced. The right (left) quotients are shown to be ideals of µ . It is proved that the right quotient ) : ( ν η r of an ideal η by an ideal ν of an L-subring µ is the largest ideal of µ such that η ν ν η ⊆ ) : ( r . 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.
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