Natural partial orders on transformation semigroups with fixed sets
type: Item
instance of: scholarly article
title: Natural partial orders on transformation semigroups with fixed sets
zbMATH Open document ID: 1472.20135
DOI: 10.1155/2016/2759090
author: Yanisa Chaiya
author: Preeyanuch Honyam
author: Jintana Sanwong
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2018-05-25T00:00:00Z
review text: Summary: Let \(X\) be a nonempty set. For a fixed subset \(Y\) of \(X\), let \(\operatorname{Fix} \left(X, Y\right)\) be the set of all self-maps on \(X\) which fix all elements in \(Y\). Then \(\operatorname{Fix} \left(X, Y\right)\) is a regular monoid under the composition of maps. In this paper, we characterize the natural partial order on \(\operatorname{Fix}(X, Y)\) and this result extends the result due to \textit{G. Kowol} and \textit{H. Mitsch} [Monatsh. Math. 102, 115--138 (1986; Zbl 0594.20062)]. Further, we find elements which are compatible and describe minimal and maximal elements.
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 6873306
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/2759090
OpenAlex ID: W2511604554
Wikidata QID: Q59124604
cites work: Q3884160
cites work: The natural partial order on a regular semigroup
cites work: A Natural Partial Order for Semigroups
cites work: Naturally ordered transformation semigroups
cites work: Q3540321
cites work: On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range
cites work: Partial orders on semigroups of partial transformations with restricted range.
cites work: Semigroups of transformations with fixed sets
cites work: Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets
cites work: The Mitsch order on a semigroup
DBLP publication ID: journals/ijmmsc/ChaiyaHS16
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description: scientific article; zbMATH DE number 6873306