Multi-transitivity of semigroup actions

2021 ◽  
pp. 1-17
Author(s):  
Huoyun Wang ◽  
Junyan Fang ◽  
Xinlin Zhong
Keyword(s):  
Semigroup Actions

Joint continuity of affine semigroup actions

1980 ◽  
Vol 21 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Dietrich Helmer
Keyword(s):  
Semigroup Actions ◽  
Joint Continuity ◽  
Affine Semigroup

Semigroup actions on ordered groupoids

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
Niovi Kehayopulu ◽  
Michael Tsingelis
Keyword(s):  
Commutative Semigroup ◽  
Equivalence Relation ◽  
Semigroup Actions ◽  
Ordered Groupoid ◽  
Quasi Order

AbstractIn this paper we prove that if S is a commutative semigroup acting on an ordered groupoid G, then there exists a commutative semigroup S̃ acting on the ordered groupoid G̃:=(G × S)/ρ̄ in such a way that G is embedded in G̃. Moreover, we prove that if a commutative semigroup S acts on an ordered groupoid G, and a commutative semigroup S̄ acts on an ordered groupoid Ḡ in such a way that G is embedded in S̄, then the ordered groupoid G̃ can be also embedded in Ḡ. We denote by ρ̄ the equivalence relation on G × S which is the intersection of the quasi-order ρ (on G × S) and its inverse ρ −1.

scholarly journals Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics

2019 ◽  
Vol 31 (3) ◽  
pp. 543-562 ◽  
Author(s):  
Viviane Beuter ◽  
Daniel Gonçalves ◽  
Johan Öinert ◽  
Danilo Royer
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Ring ◽  
Topological Dynamics ◽  
Topological Properties ◽  
Semigroup Rings ◽  
Partial Action ◽  
Semigroup Actions ◽  
Formula One ◽  
Topological Inverse Semigroup ◽  
Commutative Subring

Abstract Given a partial action π of an inverse semigroup S on a ring {\mathcal{A}} , one may construct its associated skew inverse semigroup ring {\mathcal{A}\rtimes_{\pi}S} . Our main result asserts that, when {\mathcal{A}} is commutative, the ring {\mathcal{A}\rtimes_{\pi}S} is simple if, and only if, {\mathcal{A}} is a maximal commutative subring of {\mathcal{A}\rtimes_{\pi}S} and {\mathcal{A}} is S-simple. We apply this result in the context of topological inverse semigroup actions to connect simplicity of the associated skew inverse semigroup ring with topological properties of the action. Furthermore, we use our result to present a new proof of the simplicity criterion for a Steinberg algebra {A_{R}(\mathcal{G})} associated with a Hausdorff and ample groupoid {\mathcal{G}} .

scholarly journals Algebraic entropy for amenable semigroup actions

2020 ◽  
Vol 556 ◽  
pp. 467-546
Author(s):  
Dikran Dikranjan ◽  
Antongiulio Fornasiero ◽  
Anna Giordano Bruno
Keyword(s):  
Amenable Semigroup ◽  
Semigroup Actions ◽  
Algebraic Entropy
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