TY - JOUR
T1 - Maximal and Minimal Congruences on some Semigroups
AU - Sanwong, J.
AU - Singha, B.
AU - Sullivan, Robert
PY - 2009
Y1 - 2009
N2 - 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 ℤ 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).
AB - 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 ℤ 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).
U2 - 10.1007/s10114-008-6280-7
DO - 10.1007/s10114-008-6280-7
M3 - Article
SN - 1439-8516
VL - 25
SP - 455
EP - 466
JO - Acta Mathematica Sinica-English Series
JF - Acta Mathematica Sinica-English Series
IS - 3
ER -