Monoid
A Group-like object which fails to be a Group because elements need not have an inverse within the object. Amonoid 
must also be Associative and have an Identity Element 
such that for all 
, 
. Amonoid 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. SequenceA005345/M1820in ``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.
- Exponential Sum Function
- Exponent Laws
- Exponent Vector
- Exradius
- Exsecant
- Extended Cycloid
- Extended Goldbach Conjecture
- Extended Greatest Common Divisor
- Extended Mean-Value Theorem
- Extended Riemann Hypothesis
- Extension
- Extension Problem
- Extensions Calculus
- Extent
- Exterior
- Exterior Algebra
- Exterior Angle Bisector
- Exterior Angle Theorem
- Exterior Derivative
- Exterior Dimension
- Exterior Product
- Exterior Snowflake
- Extrapolation
- Extra Strong Lucas Pseudoprime
- Extremal Coloring