Namespaces
Variants
Actions

Difference between revisions of "Reversible semi-group"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Start article: Reversible semi-group)
 
m (link)
 
Line 3: Line 3:
 
''Ore's condition''
 
''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]].
+
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