Difference between revisions of "Normal sub-semi-group"
From Encyclopedia of Mathematics
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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 [[ | + | 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 [[Monoid|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> | ||
Latest revision as of 18:31, 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=35635
Normal sub-semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_sub-semi-group&oldid=35635
This article was adapted from an original article by L.N. Shevrin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article