Open AccessOn the rank of semigroup of transformations with restricted partial range
Author(s) -
Taijie You
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2114925j
Subject(s) - mathematics , semigroup , isomorphism (crystallography) , rank (graph theory) , combinatorics , transformation (genetics) , discrete mathematics , crystallography , biochemistry , chemistry , crystal structure , gene
Let T(X) be the full transformation semigroup on a nonempty set X. For ? ? Z ? Y ? X, let T(X,Y,Z) = {? ? T(X):Y? ? 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.