View source for Reversible semi-group

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''Ore's condition''

A semi-group in which any two right [[principal ideal]]s intersect is ''left reversible'': $\forall a,b, \in S\ \exists x,y \in S \ :\ ax = by$.  A commutative semi-group is reversible, as $ab=ba$.  A semi-group which is reversible and obeys the [[cancellation law]] can be embedded in a [[group]], cf [[Imbedding of semi-groups]].

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  A.H. Clifford,   G.B. Preston,   "Algebraic theory of semi-groups" , '''1–2''' , Amer. Math. Soc.  (1961–1967)</TD></TR>
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