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    On Nilpotent Subsemigroups of the Order-Decreasing Transformation Semigroups
    (Springernature, 2023) Yagci, Melek
    For n is an element of N, let D-n be the semigroup of all order-decreasing transformations on X-n = {1, ... , n}, under its natural order, and let E(D-n) be the set of all idempotents in D-n and for any xi is an element of E(D-n), let D-n(xi) = {alpha e D-n : alpha(m) = xi for some m is an element of Z(+)}. In this paper, first we show that D-n(xi) is the maximum nilpotent subsemigroup of D-n with zero element xi. Moreover, we determine the minimum generating set of D-n(xi), and so the rank of D-n(xi). Also, we find the cardinality of D-n(xi).