Formal languages | Combinatorics on words | Semigroup theory

Compact semigroup

In mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact" here does not refer to any topology on the semigroup. Let S be a semigroup and X a finite set of letters. A system of equations is a subset E of the Cartesian product X∗ × X∗ of the free monoid (finite strings) over X with itself. The system E is satisfiable in S if there is a map f from X to S, which extends to a semigroup morphism f from X+ to S, such that for all (u,v) in E we have f(u) = f(v) in S. Such an f is a solution, or satisfying assignment, for the system E. Two systems of equations are equivalent if they have the same set of satisfying assignments. A system of equations if independent if it is not equivalent to a proper subset of itself. A semigroup is compact if every independent system of equations is finite. (Wikipedia).

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From playlist Group Theory

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From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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From playlist Course 6: Introduction to Analysis (Fall 2017)

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From playlist Group theory

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From playlist Algebraic Topology

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of the Symmetric Group

From playlist Abstract Algebra

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From playlist Dynamical Systems and Ordinary Differential Equations

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From playlist Abstract Algebra

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From playlist Abstract algebra

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From playlist Advances in Applied Probability 2019

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From playlist Winter School on Stochastic Analysis and Control of Fluid Flow

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From playlist Mathematics

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From playlist Dynamical Systems and Ordinary Differential Equations

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From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester

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From playlist Topology

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From playlist Global Noncommutative Geometry Seminar (Europe)

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From playlist Basic Algebraic Geometry

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Every Compact Set in n space is Bounded If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)

From playlist Advanced Calculus

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From playlist Probability and Statistics

Related pages

Free monoid | Topology | Semigroup | Trace monoid | Cartesian product | Free group