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.¹

References

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.

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

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