[FOM] Pre-implication algebras

[A. Mani]

What minimal algebraic conditions on a groupoid  satisfying:

(ab)a = a
(ab)b = (ba)a

would permit a concrete algebraic representation in terms of sets (like 
it happens for both implication (IA) and positive implication algebras 
(PIA))?

(The algebra generalizes concepts of ortho algebras OA and IAs, but not 
that of a positive implication algebra).

The literature on OA and generalizations do not mention much on the 
question.


Thanks and Best

A. Mani



-- 
A. Mani
CU, ASL, AMS, CLC, CMS
http://www.logicamani.in