In algebra, the '''principal factor''' of a <math>\mathcal{J}</math>-class ''J'' of a semigroup ''S'' is equal to ''J'' if ''J'' is the kernel of ''S'', and to <math>J \cup \{0\}</math> otherwise.
== Properties == * A principal factor is a simple, 0-simple or null semigroup.<ref>Grillet (1995), p. 50, Proposition 4.9.</ref>
== References == {{reflist}}
== Further reading == *{{citation|last= Howie|first= John M.|authorlink=John Mackintosh Howie|title=Fundamentals of Semigroup Theory|year=1995|publisher=Clarendon Press|isbn=0-19-851194-9}}. * {{citation|title=The algebraic theory of semigroups, volume 1|first1=A. H.|last1=Clifford|authorlink1= Alfred H. Clifford |first2=G. B.|last2=Preston|authorlink2=Gordon Preston|publisher=American Mathematical Society|year=1961}}. *{{citation|last=Grillet|first=P. A.|title=Semigroups: An Introduction to the Structure Theory|year=1995|publisher=Marcel Dekker|page=49|isbn=0824796624}}.
Category:Semigroup theory
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