Principal factor

In algebra, the principal factor of a $\mathcal{J}$ -class J of a semigroup S is equal to J if J is the kernel of S, and to $J \cup \{0\}$ otherwise.

Properties

A principal factor is a simple, 0-simple or null semigroup.Grillet (1995), p. 50, Proposition 4.9.

References

{{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

Principal factor

Properties

References

Further reading