Talk:Semigroup action

message: FYI, I have merged the entire contents of this article into semiautomaton. At this time, WP has five distinct articles (e.g. transformation semigroup, transition monoid, state transition system, etc.) all talking about exactly the same thing, all using slightly different notations and language. I'm trying to consolidate/uniformize all of these. If there are objections or comments, please leave them at Talk:Semiautomaton linas 14:23, 24 April 2007 (UTC)
replies: text: Five articles was certainly too many. However, there is a definite distinction between a semigroup action and a semiautomaton, so I've partially demerged. Further information at Talk:semiautomaton. Geometry guy 16:40, 14 September 2008 (UTC)
replies: text:  This article is written better than semiautomaton. However, every book I've looked in discusses the two notions together. To quote from Grätzer (in a similar context): "the word equivalent will not be defined". VasileGaburici (talk) 17:33, 14 September 2008 (UTC)
replies: text:  :-) However, in mathematics, we do try to define what we mean by equivalent, and there is no equivalence here! I suggest we have the discussion at Talk:semiautomaton. Geometry guy 17:39, 14 September 2008 (UTC)
replies: text:  George Grätzer is a mathematician, and the quotation is from "General Lattice Theory" where it's used in the context of the two definitions of a lattice (algebraic & order). Indeed the two notions debated here (semiautomaton/semigroup action) are not entirely equivalent. VasileGaburici (talk) 18:26, 14 September 2008 (UTC)
replies: text:  Then no doubt he tried, but decided it wasn't illuminating enough to share with his readership :-) Geometry guy 18:49, 14 September 2008 (UTC)
thread_title: Merger

message: What makes the differences is not explained. I was trying to find out the differences, but I was not able to find it. Jackzhp (talk) 20:19, 27 March 2011 (UTC)
replies: text: This is covered in Group_action#Generalizations. Every group action of G on X is a monoid action of G (regarded as a monoid) on X. --Beroal (talk) 14:01, 20 August 2011 (UTC)
thread_title: semigroup action vs. group action

message: 0. This chapter repeats stuff that is already given in the same article (e.g. "the semigroup S is a semigroup of transformations of a set X, i.e., a collection of functions from X to itself that is closed under composition. Thus S is a subsemigroup of the monoid of all transformations of X."), but omits the important stuff (how we get a transformation semigroup from a semigroup action, namely, that transformation semigroup is \{x\mapsto s\cdot x | s\in S\}). Is there a good textbook so I can rewrite the chapter referring to that textbook, i.e. without much original research?
1. IMHO this paragraph is off topic in this article: 
: Any semigroup can be realized as a transformation semigroup via an analogue of Cayley's theorem: after adjoining an identity element if necessary, the action of the semigroup on itself by (say) left multiplication is effective.
It links semigroups and transformation semigroups, while the chapter "Transformation semigroups" in the article "Semigroup action" is supposed to link semigroup actions and transformation semigroups. I want this moved to Transformation semigroup or Semigroup. Actually, it is already there.
--Beroal (talk) 14:42, 20 August 2011 (UTC)
replies: text: done --Beroal (talk) 20:20, 23 August 2011 (UTC)
thread_title:  Transformation semigroups 

message: I am definitely not an expert in this area, but I nevertheless think that the link for the term 'transformation' is not right. The link is currently transformation, but I think it should be transformation.  — Preceding unsigned comment added by 207.182.200.34 (talk) 18:09, 5 May 2015 (UTC)
thread_title:  Incorrect link for transformation term?