Centralisers in the Infinite Symmetric Inverse Semigroup
Document Type
Article
Digital Object Identifier (DOI)
10.1017/S0004972712000779
Journal Title
Bulletin of the Australian Mathematical Society
Publication Date
2013
Abstract
For an arbitrary set X (finite or infinite), denote by I(X) the symmetric inverse semigroup of partial injective transformations on X . For α∈I(X) , let C(α)={β∈I(X):αβ=βα} be the centraliser of α in I(X) . For an arbitrary α∈I(X) , we characterise the transformations β∈I(X) that belong to C(α) , describe the regular elements C(α) , and establish when C(α) is an inverse semigroup and when it is a completely regular semigroup. In the case where dom(α)=X , we determine the structure of C(α) in terms of Green’s relations.
Publisher Statement
COPYRIGHT: © 2012 Australian Mathematical Publishing Association Inc.
Published online by Cambridge University Press.
Recommended Citation
Konieczny, Janusz. “Centralisers in the Infinite Symmetric Inverse Semigroup.” Bulletin of the Australian Mathematical Society 87, no. 3 (2013): 462–79. https://doi.org/10.1017/S0004972712000779.
Comments
The definitive article is openly available on the website of the Bulletin of the Australian Mathematical Society at: https://doi.org/10.1017/S0004972712000779.
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