On Nilpotent Subsemigroups of the Order-Decreasing Transformation Semigroups
[ X ]
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springernature
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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).
Açıklama
Anahtar Kelimeler
Order-decreasing transformation, Minimum generating set, Rank, Nilpotent subsemigroups
Kaynak
Bulletin of the Malaysian Mathematical Sciences Society
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
46
Sayı
2
