Endomorphisms of semigroups of oriented transformations

De Biao Li; Vítor H. Fernandes

doi:10.1007/s00233-022-10325-y

Endomorphisms of semigroups of oriented transformations

Research output: Contribution to journal › Article › peer-review

Abstract

We characterize the monoid of endomorphisms of the semigroup of all oriented full transformations of a finite chain, as well as the monoid of endomorphisms of the semigroup of all oriented partial transformations and the monoid of endomorphisms of the semigroup of all oriented partial permutations of a finite chain. Characterizations of the monoids of endomorphisms of the subsemigroups of all orientation-preserving transformations of the three semigroups aforementioned are also given. In addition, we compute the number of endomorphisms of each of these six semigroups.

Original language	English
Journal	Semigroup Forum
DOIs	https://doi.org/10.1007/s00233-022-10325-y
Publication status	Published - 2022

Keywords

Endomorphisms
Orientation-preserving
Orientation-reversing
Oriented
Transformations

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10.1007/s00233-022-10325-y

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abstract = "We characterize the monoid of endomorphisms of the semigroup of all oriented full transformations of a finite chain, as well as the monoid of endomorphisms of the semigroup of all oriented partial transformations and the monoid of endomorphisms of the semigroup of all oriented partial permutations of a finite chain. Characterizations of the monoids of endomorphisms of the subsemigroups of all orientation-preserving transformations of the three semigroups aforementioned are also given. In addition, we compute the number of endomorphisms of each of these six semigroups.",

keywords = "Endomorphisms, Orientation-preserving, Orientation-reversing, Oriented, Transformations",

author = "Li, {De Biao} and Fernandes, {V{\'i}tor H.}",

note = "Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT# This work is partially supported by the National Natural Science Foundation of China (nos. 12271224, 12171213) and by China Scholarship Council to visit Universidade Nova de Lisboa. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s00233-022-10325-y",

language = "English",

journal = "Semigroup Forum",

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T1 - Endomorphisms of semigroups of oriented transformations

AU - Li, De Biao

AU - Fernandes, Vítor H.

N1 - Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT# This work is partially supported by the National Natural Science Foundation of China (nos. 12271224, 12171213) and by China Scholarship Council to visit Universidade Nova de Lisboa. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - We characterize the monoid of endomorphisms of the semigroup of all oriented full transformations of a finite chain, as well as the monoid of endomorphisms of the semigroup of all oriented partial transformations and the monoid of endomorphisms of the semigroup of all oriented partial permutations of a finite chain. Characterizations of the monoids of endomorphisms of the subsemigroups of all orientation-preserving transformations of the three semigroups aforementioned are also given. In addition, we compute the number of endomorphisms of each of these six semigroups.

AB - We characterize the monoid of endomorphisms of the semigroup of all oriented full transformations of a finite chain, as well as the monoid of endomorphisms of the semigroup of all oriented partial transformations and the monoid of endomorphisms of the semigroup of all oriented partial permutations of a finite chain. Characterizations of the monoids of endomorphisms of the subsemigroups of all orientation-preserving transformations of the three semigroups aforementioned are also given. In addition, we compute the number of endomorphisms of each of these six semigroups.

KW - Endomorphisms

KW - Orientation-preserving

KW - Orientation-reversing

KW - Oriented

KW - Transformations

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U2 - 10.1007/s00233-022-10325-y

DO - 10.1007/s00233-022-10325-y

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AN - SCOPUS:85143238091

SN - 0037-1912

JO - Semigroup Forum

JF - Semigroup Forum

ER -

Endomorphisms of semigroups of oriented transformations

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Keywords

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