TY - JOUR
T1 - On Semigroups of Orientation-preserving Transformations with Restricted Range
AU - Fernandes, Vítor H.
AU - Honyam, Preeyanuch
AU - Quinteiro, Teresa M.
AU - Singha, Boorapa
N1 - FCT of CAUL (PEst-OE/MAT/UI0143/2014)
PY - 2016/1/2
Y1 - 2016/1/2
N2 - Let X n be a chain with n elements (n ∈ ℕ), and let 𝒪𝒫 n be the monoid of all orientation-preserving transformations of X n. In this article, for any nonempty subset Y of X n, we consider the subsemigroup 𝒪𝒫 n(Y) of 𝒪𝒫 n of all transformations with range contained in Y: We describe the largest regular subsemigroup of 𝒪𝒫 n(Y), which actually coincides with its subset of all regular elements. Also, we determine when two semigroups of the type 𝒪𝒫 n(Y) are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid 𝒪ℛ n of all either orientation-preserving or orientation-reversing transformations of X n.
AB - Let X n be a chain with n elements (n ∈ ℕ), and let 𝒪𝒫 n be the monoid of all orientation-preserving transformations of X n. In this article, for any nonempty subset Y of X n, we consider the subsemigroup 𝒪𝒫 n(Y) of 𝒪𝒫 n of all transformations with range contained in Y: We describe the largest regular subsemigroup of 𝒪𝒫 n(Y), which actually coincides with its subset of all regular elements. Also, we determine when two semigroups of the type 𝒪𝒫 n(Y) are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid 𝒪ℛ n of all either orientation-preserving or orientation-reversing transformations of X n.
KW - Orientation-preserving
KW - Orientation-reversing
KW - Rank
KW - Restricted range
KW - Transformations
UR - http://www.scopus.com/inward/record.url?scp=84944790117&partnerID=8YFLogxK
U2 - 10.1080/00927872.2014.975345
DO - 10.1080/00927872.2014.975345
M3 - Article
AN - SCOPUS:84944790117
VL - 44
SP - 253
EP - 264
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 1
ER -