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 congruences on the semigroup . n under 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