Feeling less-than-brilliant....

[patrickwonders]

On the bus ride home last night, I started reading Algebras, Lattices, Varieties by McKenzie, McNulty, and Taylor. I felt like I was flying through the first chapter until they threw in the line that all monoids are extensions of semigroups but not all semigroups can be extended into monoids.

Comments

[mathnerdguy]

Wikipedia (fourth bullet point) says that your book is lying.

[patrickwonders]

Whee. I haven't had the book with me since this time last night. Now, I am chomping at the bit to go reread it and make sure I am clear on what it said. It was both a statement in the text and then an exercise to exhibit such a semigroup.

[patrickwonders]

Well, I misread the context. Expansion is accomplished by adjoining operators (in this case, a nullary operator to distinguish an element of the set) not by adjoining elements. It's much easier now. Thanks.