
Maximal subsemigroups and the maximal regular subsemigroups of the semigroup H ^{*}_{(n,m)}(r)
 YUAN Yue, ZHAO Ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(12):
1924.
doi:10.6040/j.issn.16719352.0.2020.319

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Let T_{n} be the full transformation semigroup on X_{n}={1,2,…,n}. For any 1≤m≤n1, let X_{m}={1,2,…,m}. Through the subsemigroupsG_{(n,m)}={α∈T_{(n,m)}:(X_{n}\X_{m})α=X_{n}\X_{m}}andH_{(n,m)}={α∈T_{(n,m)}:(X_{n}\X_{m})α⊆X_{n}\X_{m}}of the semigroup T_{(n,m)}={α∈T_{n}:X_{m}α=X_{m}}, the subsemigroups of the semigroup H ^{*}_{(n,m)}(r)={α∈H_{(n,m)}:im(α)≤r}∪G_{(n,m)} are studied for 1≤m<r≤n1, and it is proved that the maximal subsemigroups of H ^{*}_{(n,m)}(r)are the same as the maximal regular subsemigroups.