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...group") is a [[completely regular semigroup|completely regular]] [[inverse semigroup]]. It is an inverse semigroup with<ref>[http://www-circa.mcs.st-and.ac.uk/Theses/cacmsc.pdf Presentations ...

...he '''principal factor''' of a <math>\mathcal{J}</math>-class ''J'' of a [[semigroup]] ''S'' is equal to ''J'' if ''J'' is the [[kernel (algebra)|kernel]] of '' ...principal factor is a [[Simple semigroup|simple]], [[0-simple]] or [[null semigroup]].<ref>Grillet (1995), p. 50, Proposition 4.9.</ref> ...

...isomorphisms between principal ideals of a [[semilattice]] (a commutative semigroup of idempotents). Munn semigroups are named for the Scottish mathematician [ 3) The Munn semigroup of the [[semilattice]] ''E'' is defined as: ''T''_''E'' :=&nbsp; ...

[[File:Monogenic semigroup order 9 period 6.gif|thumb|500px|Monogenic semigroup of order 9 and period 6. Numbers are exponents of the generator ''a''; arro ...<ref>{{cite book|last=A H Clifford|author2=G B Preston|title=The Algebraic Theory of Semigroups Vol.I|publisher=American Mathematical Society|year=1961|serie ...

...semigroup]] theory, a '''nilsemigroup''' or '''nilpotent semigroup''' is a semigroup whose every element is [[nilpotent]]. Formally, a semigroup ''S'' is a nilsemigroup if: ...

...are completely 0-simple [[inverse semigroup]]s. In other words, they are [[semigroup]]s without proper ideals and which are also inverse semigroups. They are bu Then, it can be shown that every 0-simple semigroup is of the form <math>S = (I\times G^0\times J)</math> with the operation <m ...

...=2005|publisher=Springer}}</ref> Various generalizations of the 3''x'' + 1 semigroup have been constructed and their properties have been investigated.<ref name The 3''x'' + 1 semigroup is the multiplicative semigroup of positive rational numbers [[generator (mathematics)|generated]] by the s ...

...008|p=v}}</ref> In general <math>\mathcal{I}_X</math> is not [[Commutative semigroup|commutative]]. ...n the discussion on the [[Inverse_semigroup#Origins|origins of the inverse semigroup]]. ...

...t has a power that belongs to a [[subgroup]]. Formally, for all ''x'' in a semigroup ''S'', there exists a positive [[integer]] ''n'' and a subgroup ''G'' of '' ...07">{{cite book|author1=Eric Jespers|author2=Jan Okninski|title=Noetherian Semigroup Algebras|url=https://books.google.com/books?id=qzj3MkWnCLQC&pg=PA16|year=20 ...

== Partial semigroup == ...name="Schelp">{{cite journal |last1=Schelp |first1=R. H. |title=A partial semigroup approach to partially ordered sets |journal=Proceedings of the London Mathe ...

...] constructed using a semigroup and an [[ideal of a semigroup|ideal of the semigroup]]. ...ntity. The new semigroup obtained in this way is called the '''Rees factor semigroup of ''S'' modulo ''I'' ''' and is denoted by ''S''/''I''. ...

...five idempotent elements has also been studied along with the four-spiral semigroup.<ref name="Meakin"/><ref name="Grillet"/> The four-spiral semigroup, denoted by ''Sp₄'', is the [[free semigroup]] generated by four elements ''a'', ''b'', ''c'', and ''d'' satisfying th ...

{{Short description|Example of a Semigroup}} In [[mathematics]], a '''semigroup with two elements''' is a [[semigroup]] for which the [[cardinality]] of the [[underlying set]] is two. There are ...

...a '''transformation''' (or '''composition''') '''monoid'''. This is the [[semigroup]] analogue of a [[permutation group]]. ...actions are characterized by being faithful, i.e., if two elements of the semigroup have the same action, then they are equal. ...

A [[semigroup]] of linear operators can be strongly measurable yet not strongly continuou [[Category:Semigroup theory]] ...

...near]] or non-linear. Closely related to Markov operators is the '''Markov semigroup'''.<ref name="BGL">{{cite book|title=Analysis and Geometry of Markov Diffus ...gyu|last=Wang|title=Functional Inequalities Markov Semigroups and Spectral Theory|place=Ukraine|publisher=Elsevier Science|date=2006|page=3}}</ref> ...

...l notions. Varieties of finite [[monoid]]s, varieties of finite [[ordered semigroup]]s and varieties of finite [[ordered monoid]]s are defined similarly. *is closed under [[Semigroup#Quotients and divisions|division]]. ...

...h>f=0</math>) case with a constant operator is given by the theory of [[C0-semigroup|C₀-semigroups]]. Very often, the study of other abstract differe The theory of abstract differential equations has been founded by [[Einar Hille]] in s ...

{{Short description|Operator in analysis and probability theory}} ...The {{Lang|fr|carré du champ operator|italic=no}} measures how far an [[C0-semigroup#Infinitesimal generator|infinitesimal generator]] is from being a [[Derivat ...

...ne of these languages determines "canonical forms" for the elements of the semigroup, the other languages determine if two canonical forms represent elements th Formally, let <math>S</math> be a semigroup and <math>A</math> be a finite set of generators. Then an ''automatic stru ...