Principal factor

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

Properties

• A principal factor is a simple, 0-simple or null semigroup.

Further reading

• Howie, John M. (1995), Fundamentals of Semigroup Theory, Clarendon Press, ISBN 0-19-851194-9 .
• Clifford, A. H.; Preston, G. B. (1961), The algebraic theory of semigroups, volume 1, American Mathematical Society .
• Grillet, P. A. (1995), Semigroups: An Introduction to the Structure Theory, Marcel Dekker, p. 49, ISBN 0824796624 .