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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th-cmuir.6653943832-492522018-08-16T02:13:17Z Maximal and minimal congruences on some semigroups Jintana Sanwong Boorapa Singha R. P. Sullivan Mathematics 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. 2018-08-16T02:13:17Z 2018-08-16T02:13:17Z 2009-03-01 Journal 14398516 2-s2.0-63849105958 10.1007/s10114-008-6280-7 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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Mathematics |
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Mathematics Jintana Sanwong Boorapa Singha R. P. Sullivan Maximal and minimal congruences on some semigroups |
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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. |
| format |
Journal |
| author |
Jintana Sanwong Boorapa Singha R. P. Sullivan |
| author_facet |
Jintana Sanwong Boorapa Singha R. P. Sullivan |
| author_sort |
Jintana Sanwong |
| title |
Maximal and minimal congruences on some semigroups |
| title_short |
Maximal and minimal congruences on some semigroups |
| title_full |
Maximal and minimal congruences on some semigroups |
| title_fullStr |
Maximal and minimal congruences on some semigroups |
| title_full_unstemmed |
Maximal and minimal congruences on some semigroups |
| title_sort |
maximal and minimal congruences on some semigroups |
| publishDate |
2018 |
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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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