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|Title:||Maximal and minimal congruences on some semigroups|
R. P. Sullivan
|Abstract:||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.|
|Appears in Collections:||CMUL: Journal Articles|
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