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.

• Tree-Planting Problem
• Tree Searching
• Trefoil Curve
• Trefoil Knot
• Trench Diggers' Constant
• Triabolo
• Triacontagon
• Triacontahedron
• Triad
• Triakis Icosahedron
• Triakis Octahedron
• Triakis Tetrahedron
• Trial
• Trial Division
• Trial Divisor
• Triamond
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• Triangle Arcs
• Triangle Center
• Triangle Center Function
• Triangle Coefficient
• Triangle Condition
• Triangle Counting
• Triangle Function
• Triangle Inequality