Open Access
2015 On De Graaf spaces of pseudoquotients
Anya Katsevich, Piotr Mikusiński
Rocky Mountain J. Math. 45(5): 1445-1455 (2015). DOI: 10.1216/RMJ-2015-45-5-1445


A space of pseudoquotients, $\mathcal{B}(X,S)$, is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and $(x,f) \sim (y,g)$ if $gx=fy$. In this note, we consider a generalization of this construction where the assumption of commutativity of $S$ is replaced by Ore type conditions. As in the commutative case, $X$ can be identified with a subset of $\mathcal{B}(X,S)$, and $S$ can be extended to a group, $G$, of bijections on $\mathcal{B}(X,S)$. We introduce a natural topology on $\mathcal{B}(X,S)$ and show that all elements of $G$ are homeomorphisms on $\mathcal{B}(X,S)$.


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Anya Katsevich. Piotr Mikusiński. "On De Graaf spaces of pseudoquotients." Rocky Mountain J. Math. 45 (5) 1445 - 1455, 2015.


Published: 2015
First available in Project Euclid: 26 January 2016

zbMATH: 1348.44008
MathSciNet: MR3452222
Digital Object Identifier: 10.1216/RMJ-2015-45-5-1445

Primary: 44A40
Secondary: 16U20

Keywords: Ore condition , Ore localization , Pseudo quotients , semigroup action

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.45 • No. 5 • 2015
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