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Difference between revisions of "Normal sub-semi-group"

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''of a semi-group $S$''
 
''of a semi-group $S$''
  
A sub-semi-group $H$ satisfying the following condition: For any $x,y\in S^1$ (for the notation $S^1$ see [[Normal complex|Normal complex]]) such that $xy\in S$ and for any $h\in H$ the relations $xhy\in H$ and $xy\in H$ are equivalent. A subset of $S$ is a normal sub-semi-group if and only if it is the complete inverse image of the unit element under some homomorphism of $S$ onto a [[Semi-group|semi-group]] with unit element.
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A sub-semi-group $H$ satisfying the following condition: For any $x,y\in S^1$ (for the notation $S^1$ see [[Normal complex|Normal complex]]) such that $xy\in S$ and for any $h\in H$ the relations $xhy\in H$ and $xy\in H$ are equivalent. A subset of $S$ is a normal sub-semi-group if and only if it is the complete inverse image of the [[unit element]] under some homomorphism of $S$ onto a [[Monois|semi-group with unit element]].
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  E.S. Lyapin,  "Semigroups" , Amer. Math. Soc.  (1974)  (Translated from Russian)</TD></TR></table>
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  E.S. Lyapin,  "Semigroups" , Amer. Math. Soc.  (1974)  (Translated from Russian)</TD></TR></table>

Revision as of 18:30, 13 December 2014

of a semi-group $S$

A sub-semi-group $H$ satisfying the following condition: For any $x,y\in S^1$ (for the notation $S^1$ see Normal complex) such that $xy\in S$ and for any $h\in H$ the relations $xhy\in H$ and $xy\in H$ are equivalent. A subset of $S$ is a normal sub-semi-group if and only if it is the complete inverse image of the unit element under some homomorphism of $S$ onto a semi-group with unit element.

References

[1] E.S. Lyapin, "Semigroups" , Amer. Math. Soc. (1974) (Translated from Russian)
How to Cite This Entry:
Normal sub-semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_sub-semi-group&oldid=32024
This article was adapted from an original article by L.N. Shevrin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article