# Reversible semi-group

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 20M [MSN][ZBL]

*Ore's condition*

A semi-group in which any two right principal ideals 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

[1] | A.H. Clifford, G.B. Preston, "Algebraic theory of semi-groups" , 1–2 , Amer. Math. Soc. (1961–1967) |

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Reversible semi-group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Reversible_semi-group&oldid=39357