History of Semigroup

Difference (from prior major revision) (author diff)

Changed: 7c7

* The positive integers with addition.

Added: 17a18,21

The intersection of two ideals is also an ideal, so a semigroup can have at most one minimal ideal.
All nonempty finite semigroups have a minimal ideal.
An example of semigroup with no minimal ideal is the set of positive integers under addition.
The minimal ideal of a commutative semigroup, when it exists, is a group.

	Revision 17 . . October 5, 2001 4:48 am by Zundark [some notes on the minimal ideal]
	Revision 16 . . October 5, 2001 1:43 am by Zundark [periodic semigroups]
	Revision 15 . . (edit) October 5, 2001 1:33 am by Zundark [to-sided -> two-sided]
	Revision 14 . . October 5, 2001 12:18 am by AxelBoldt [remove repetition, one more example]
	Revision 13 . . (edit) October 4, 2001 10:43 pm by Zundark [mention uniqueness of the idempotent of a finite cyclic semigroup, and fix a typo]
	Revision 12 . . (edit) September 9, 2001 7:24 am by Zundark [add link]