left inverse

left inverse

[¦left in¦vərs]
(mathematics)
For a set S with a binary operation x · y that has an identity element e, the left inverse of a member, x, of S is another member, , of S for which · x = e.
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References in periodicals archive ?
Similarly, it is called a left inverse property quasigroup (loop) [LIPQ (LIPL)] if and only if it obeys the left inverse property (LIP) [x.
Similarly, it is called a second Smarandache left inverse property quasigroup (loop) [[S.
A quasigroup (Q, -)has the left inverse property,the right inverse property or the cross inverse property, if for any x [member of] Q there exists an element x-1 such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
A loop is called a Smarandache left inverse property loop (SLIPL) if it has at least a non-trivial subloop with the LIP.
Left Bol loops have the left inverse property(LIP), hence, (S, [direct sum]) and (S, [?