Principal factor

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

Properties

• A principal factor is a simple, 0-simple or null semigroup.^[1]

References

1. Grillet (1995), p. 50, Proposition 4.9.

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.