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.
- Trivialization
- Trochoid
- Tromino
- True
- Truncate
- Truncated Cone
- Truncated Cube
- Truncated Cuboctahedron
- Truncated Dodecadodecahedron
- Truncated Dodecahedron
- Truncated Great Dodecahedron
- Truncated Great Icosahedron
- Truncated Hexahedron
- Truncated Icosahedron
- Truncated Icosidodecahedron
- Truncated Octahedral Number
- Truncated Octahedron
- Truncated Polyhedron
- Truncated Pyramid
- Truncated Square Pyramid
- Truncated Tetrahedral Number
- Truncated Tetrahedron
- Truncation
- Truth Table
- Tschebyshev