How to handle partial transformations

Journal article

A number of concepts in modern algebra have arisen as abstract versions of systems of functions of one type or another, the most famous example of course being groups: the abstractions of systems of bijections or permutations. Going further, the articulation in the 1920s and 1930s of the fact that non-invertible transformations are no less ubiquitous than bijective ones, led to the abstraction of systems of arbitrary transformations and the beginning of the theory of semigroups. Various other types of functions have also been studied in a similar manner. One particularly interesting instance, though one that is arguably lesser known, is that of partial transformations. In this article, I give a taste of the study of partial transformations and the corresponding abstract theory.

Authors: Hollings, C

• Publication status: Published
• Peer review status: Reviewed (other)
• Publisher: Institute of Mathematics and its Applications
• Journal: Mathematics Today
• Volume: 53
• Issue: 3
• Pages: 121–123
• Publication date: 2017-01-01
• Acceptance date: 2016-06-30
• ISSN: 1361-2042