Semigroup
A mathematical object defined for a set and a Binary Operator in which the multiplication operation isAssociative. No other restrictions are placed on a semigroup; thus a semigroup need not have an IdentityElement and its elements need not have inverses within the semigroup. A semigroup is an Associative Groupoid.
A semigroup can be empty. The total number of semigroups of order 
are 1, 4, 18, 126, 1160, 15973, 836021, ...(Sloane's A001423). The number of semigroups of order with one Idempotent are 1, 2, 5, 19, 132, 3107, 623615, ...(Sloane's A002786), and with two A002787). Thenumber 
of semigroups having A002788).
References
Clifford, A. H. and Preston, G. B. The Algebraic Theory of Semigroups. Providence, RI: Amer. Math. Soc., 1961. Sloane, N. J. A. SequencesA001423/M3550,A002786/M1522,A002787/M1802, andA002787/M1679in ``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.
- Multifactorial
- Multifractal Measure
- Multigrade Equation
- Multilinear
- Multimagic Series
- Multimagic Square
- Multinomial Coefficient
- Multinomial Distribution
- Multinomial Series
- Multinomial Theorem
- Multiperfect Number
- Multiple Integral
- Multiple Regression
- Multiplication
- Multiplication Magic Square
- Multiplication Principle
- Multiplication Sign
- Multiplication Table
- Multiplicative Character
- Multiplicative Digital Root
- Multiplicative Function
- Multiplicative Inverse
- Multiplicative Perfect Number
- Multiplicative Persistence
- Multiplicative Primitive Residue Class Group