Difference between revisions of "Reversible semi-group"
From Encyclopedia of Mathematics
(Start article: Reversible semi-group) |
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| − | A semi-group in which any two right principal | + | 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==== | ====References==== | ||
Latest revision as of 11:41, 2 October 2016
2020 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) |
How to Cite This Entry:
Reversible semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reversible_semi-group&oldid=35847
Reversible semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reversible_semi-group&oldid=35847