Maximal and minimal congruences on some semigroups
In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T(X) consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruenc...
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| Main Authors: | , , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=63849105958&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49252 |
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| Institution: | Chiang Mai University |
| Summary: | In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T(X) consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup ℤnunder multiplication modulo n. And, when Y ⊆ X, we do the same for the semigroup T(X, Y) consisting of all elements of T(X) whose range is contained in Y. We also characterise the minimal congruences on T(X, Y). © 2009 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH. |
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