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5:01
Algebraic System - Binary Operations, Semi-Group & Monoid
Complete set of Video Lessons and Notes available only at http://www.studyyaar.com/index.p...
published: 11 Oct 2013
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60:44
Reactive Game Development For The Discerning Hipster By Bodil Stokke
Norfolk Developers 2nd of July 2014. Reactive Game Development For The Discerning Hipster...
published: 30 Sep 2014
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14:55
A survey of Dr. Qaiser Mushtaq's research in coset diagrams1.mp4
Qaiser Mushtaq (born: February 28, 1954), (D.Phil., ASA, KIA), is a prominent Pakistani ma...
published: 14 Oct 2011
author: algebraforum
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4:19
Tres Armas Kali Academy (Chicago Illinois)
Tres Armas Kali is a combat ready weapons and empty hand based self defense martial arts s...
published: 25 Feb 2012
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77:14
Markov loops ensembles
Any semigroup of Markovian transition kernels defines a sigma-finite measure on loops whic...
published: 17 Jul 2013
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2:42
Young Talent Video: East Coast - 2020
Imagine a walk in East Coast Park 8 years from now, as modern technology enhances our life...
published: 06 Apr 2012
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108:32
Mikhael Gromov - 2/6 Probability, symmetry, linearity
I plan six lectures on possible directions of modification/generalization of the probabili...
published: 17 Oct 2014
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97:13
Mikhael Gromov - 6/6 Probability, symmetry, linearity
I plan six lectures on possible directions of modification/generalization of the probabili...
published: 14 Nov 2014
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0:28
Quonset hut Designs - Metal Building Design for a Modern Age
Read history and advantages of Quonset hut, and find how Quonset hut is beneficial for you...
published: 07 Oct 2014
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13:03
Modern Algebra (Abstract Algebra) Made Easy - Part 0 - the Binary Operation
http://www.pensieve.net/course/13 In this video, I introduce the binary operation, and giv...
published: 01 Aug 2012
author: scalenescott
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20:58
Lesson 5-English -Algebra-Volume IV
Groups Monoizi Definition: A nonempty monoid M is compared with a composition law defined ...
published: 29 Mar 2014
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5:35
Groups - Showing G is a group - Part 1
Groups - Showing G is a group - Part 1 For more free math videos, visit http://JustMathTut...
published: 25 Oct 2008
author: patrickJMT
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Groups - Showing G is a group - Part 2
Groups - Showing G is a group - Part 2 For more free math videos, visit http://JustMathTut...
published: 25 Oct 2008
author: patrickJMT
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1:28
Volleyball Drills Pack Review
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published: 06 Dec 2008
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Biking in Southern Estonia in summer 2012
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published: 06 Oct 2012
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ChaosBook chapter "Cycle stability", part 2
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published: 22 Jan 2014
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Binary Operations part 2.mp4
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published: 20 Oct 2011
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"Colorful Breathless" - fast pace Indian semiclassical dance
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published: 08 Sep 2011
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61:31
3 Nandakumaran - An Introduction to deterministic optimal control and controllability
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Alessandra Palmigiano: "Groupoid quantales beyond the etale setting"
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46:47
Spoils of the Egyptians: Lecture 1 Part 1
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published: 02 Nov 2012
author: A9 Videos
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48:01
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published: 08 Jan 2013
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Mod-03 Lec-12 The Monodromy Action
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58:28
The representation theory of triangularizable monoids
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published: 18 Feb 2012
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Functional Analysis - Lecture 24 - UCCS MathOnline
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published: 16 Feb 2012
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Group Homomorphisms
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In abstract algebra, the free monoid on a set A is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from A. It is usually denoted A. The identity element is the unique sequence of zero elements, often called the empty string and denoted by ε or λ, and the monoid operation is string concatenation. The free semigroup on A is the subsemigroup of A containing all elements except the empty string. It is usually denoted A+.

More generally, an abstract monoid (or semigroup) S is described as free if it is isomorphic to the free monoid (or semigroup) on some set.

As the name implies, free monoids and semigroups are those objects which satisfy the usual universal property defining free objects, in the respective categories of monoids and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). The study of semigroups as images of free semigroups is called combinatorial semigroup theory.

The members of a set A are called the free generators for A and A+. The superscript * is then commonly understood to be the Kleene star. More generally, if S is an abstract free monoid (semigroup), then a set of elements which maps onto the set of single-letter words under an isomorphism to a semigroup A+ (monoid A) is called a set of free generators for S.




This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Free_monoid

This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.