Difference between revisions of "Normal complex"
From Encyclopedia of Mathematics
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| − | ''of a semi-group | + | {{TEX|done}} |
| + | ''of a semi-group $S$'' | ||
| − | A non-empty subset | + | A non-empty subset $N\subseteq S$ satisfying the following condition: For any $x,y\in S^1$ (where $S^1=S$ when $S$ contains a unit element and $S^1$ is the semi-group obtained from $S$ by adjoining a unit element if $S$ does not have one) and any $a,b\in N$ it follows from $xay\in N$ that $xby\in N$. A subset $N$ is a normal complex of a semi-group $S$ if and only if $N$ is a class of some congruence on $S$ (cf. [[Congruence (in algebra)|Congruence (in algebra)]]). |
====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 20:27, 14 April 2014
of a semi-group $S$
A non-empty subset $N\subseteq S$ satisfying the following condition: For any $x,y\in S^1$ (where $S^1=S$ when $S$ contains a unit element and $S^1$ is the semi-group obtained from $S$ by adjoining a unit element if $S$ does not have one) and any $a,b\in N$ it follows from $xay\in N$ that $xby\in N$. A subset $N$ is a normal complex of a semi-group $S$ if and only if $N$ is a class of some congruence on $S$ (cf. Congruence (in algebra)).
References
| [1] | E.S. Lyapin, "Semigroups" , Amer. Math. Soc. (1974) (Translated from Russian) |
How to Cite This Entry:
Normal complex. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_complex&oldid=13821
Normal complex. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_complex&oldid=13821
This article was adapted from an original article by L.N. Shevrin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article