A Group-like object which fails to be a Group because elements need not have an inverse within the object. A monoid must also be Associative and have an Identity Element such that for all , . A monoid is therefore a Semigroup with an Identity Element. A monoid must contain at least one element.

The numbers of free idempotent monoids on letters are 1, 2, 7, 160, 332381, ... (Sloane's A005345).

**References**

Rosenfeld, A. *An Introduction to Algebraic Structures.* New York: Holden-Day, 1968.

Sloane, N. J. A. Sequence
A005345/M1820
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26