Geodesic
On the rank of semigroup of transformations with restricted partial range
Filomat, Tome 35 (2021) no. 14, p. 4925

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DOI

Let T (X) be the full transformation semigroup on a nonempty set X. For ∅ Z ⊆ Y ⊆ X, let T (X, Y, Z) = {α ∈ T (X) : Yα ⊆ Z}. It is not difficult to see that it is a generalized form of three well-known semigroups. This paper obtains an isomorphism theorem of T (X, Y, Z). In addition, when X is finite and Z ⊂ Y ⊂ X, the rank of the semigroup T (X, Y, Z) is calculated
DOI : 10.2298/FIL2114925J
Classification : 20M20
Keywords: transformation semigroup, rank, restricted range, isomorphism theorem 
Jiulin Jin. On the rank of semigroup of transformations with restricted partial range. Filomat, Tome 35 (2021) no. 14, p. 4925 . doi: 10.2298/FIL2114925J
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     author = {Jiulin Jin},
     title = {On the rank of semigroup of transformations with restricted partial range},
     journal = {Filomat},
     pages = {4925 },
     year = {2021},
     volume = {35},
     number = {14},
     doi = {10.2298/FIL2114925J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2114925J/}
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