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On a set of generating relations of the full transformation semigroups

1974
*
Journal of combinatorial theory. Series A
*

*A*

*set*

*of*

*generating*

*relations*

*of*

*the*

*full*

*transformation*

*semigroup*Z% consisting

*of*all mappings

*of*

*the*

*set*Sz = {l,..., n} into itself with respect to

*a*natural system

*of*

*generators*{yji, uji} (defined ...

*The*

*set*

*of*

*relations*(1)~(15) given in Section 1 turns out to be

*a*

*set*

*of*

*generating*

*relations*. ...

*THE*

*SEMIGROUP*Zn Let Q = Q, be

*the*

*set*{I,..., n}. We denote by .Zn

*the*

*semigroup*consisting

*of*all mappings

*of*1;2 into 1;2 with

*the*multiplication

*of*mapping composition. ...

##
###
NUMERICAL AND GRAPHICAL RESULTS OF FINITE SYMMETRIC INVERSE (I_{n}) AND FULL (T_{n}) TRANSFORMATION SEMIGROUPS

2021
*
FUDMA Journal of Sciences
*

*full*

*transformation*

*semigroup*

*of*degree , as well as their respective powers for

*a*given fixed time in space. ... Supposed is

*a*finite

*set*, then

*a*function is called

*a*finite partial

*transformation*

*semigroup*, which moves elements

*of*from its domain to its co-domain by

*a*distance

*of*where . ...

*The*

*set*

*of*all partial functions

*on*

*a*given base

*set*, forms

*a*regular

*Semigroup*called

*the*

*Semigroup*

*of*all partial

*transformations*(or

*the*partial

*transformation*

*Semigroup*

*on*), typically denoted by ...

##
###
Generation of diagonal acts of some semigroups of transformations and relations

2005
*
Bulletin of the Australian Mathematical Society
*

*The*

*semigroup*

*of*

*full*finiteto-

*one*

*transformations*

*on*an infinite

*set*has

*a*cyclic diagonal right act but its diagonal left act is not finitely

*generated*. ... We show that

*the*

*semigroups*

*of*

*full*

*transformations*, partial

*transformations*and binary

*relations*

*on*an infinite

*set*each have cyclic diagonal right and left acts. ... Theorem 3. 4 . 4

*The*diagonal left act

*of*F X ,

*the*

*semigroup*

*of*

*full*finite-to-

*one*

*transformations*

*on*an infinite

*set*X, is not finitely

*generated*. ...

##
###
Page 1206 of Mathematical Reviews Vol. 47, Issue 5
[page]

1974
*
Mathematical Reviews
*

*The*question whether

*the*Green

*relations*in End R are restrictions

*of*those in

*the*

*full*

*transformation*

*semigroups*7,

*on*R regarded as

*a*

*set*, is decided in

*the*affirmative for rings R in case 2 above, but ... Let [ be

*the*

*semigroup*

*of*all (partial)

*transformations*

*of*

*a*

*set*Q into

*a*proper subset Q,. Let I’, [[',] be

*the*subsemi- group

*of*I’

*generated*by all (

*full*) idempotent transforma- tions from I’. ...

##
###
Page 554 of Mathematical Reviews Vol. 36, Issue 3
[page]

1968
*
Mathematical Reviews
*

*The*

*full*

*transformation*

*semigroup*7',

*on*

*a*

*set*X consists

*of*all mappings

*of*X into itself together with

*the*operation

*of*composition. ... In fact, H,-

*semigroup*is

*a*

*generalization*

*of*p-

*semigroup*. T. Tamura (Davis, Calif.) Howie, J. M. 2728

*The*subsemigroup

*generated*by

*the*idempotents

*of*

*a*

*full*

*transformation*

*semigroup*. J. London Math. ...

##
###
Page 8667 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

*The*authors describe products

*of*arbitrary Y-, Z- and #-classes with

*the*

*set*E

*of*idempotents

*of*

*full*

*transformation*

*semigroups*. ... For

*a*

*set*X, denote by By

*the*

*semigroup*

*of*binary

*relations*

*on*X. Let D be

*a*complete X-semilattice

*of*unions, that is,

*a*nonempty family

*of*subsets

*of*X that is closed under

*set*-theoretic unions. ...

##
###
Page 6215 of Mathematical Reviews Vol. , Issue 98J
[page]

1998
*
Mathematical Reviews
*

Green’s

*relations*in S~(X) are characterized and their star analogues are shown to be*the*respective restrictions*of*Green’s*relations*in 7(X),*the**full**transformation**semigroup**on*X. ...*The*author establishes some results*related*to*the**generalized*Green’s*relations**on*m-regular*semigroups*, which elsewhere in*the*literature are known as eventually regular*semigroups*[see P. M. ...##
###
On Divisors of Pseudovarieties Generated by Some Classes of Full Transformation Semigroups

2008
*
Algebra Colloquium
*

*The*pseudovariety OP

*generated*by all

*semigroups*

*of*orientation-preserving

*full*

*transformations*

*on*

*a*finite chain was studied by Catarino and Higgins in [6] . ... ]

*full*

*transformations*

*on*

*a*finite chain. ...

*full*

*transformations*

*on*

*a*finite chain. ...

##
###
Ranks of Identity Difference Transformation Semigroup

2022
*
International journal of pure mathematics
*

This study focuses

doi:10.46300/91019.2022.9.10
fatcat:3ndcqzzcz5grbfp3tixvbhvvwy
*on**the*ranks*of*identity difference*transformation**semigroup*. ...*The*ideals*of*all*the*(sub)*semigroups*; identity difference*full**transformation**semigroup*(IDT_n), identity difference order preserving*transformation**semigroup*, (IDO_n), identity difference symmetric ... INTRODUCTION*The*rank*of**transformation**semigroup**on**a**set*𝑋 𝑛 has been widely studied. ...##
###
Page 170 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

(English and Chinese summaries)
Guizhou Shifan Daxue Xuebao Ziran Kexue Ban 18 (2000), no. 4, 64-69
Let 7, denote

*the**full**transformation**semigroup**on**the**set*X {1,2,...,*a*}. ... It is shown that*the*rank*of**A*@¥,, (that is,*the*minimal size*of**a**generating**set*) is n, and*a*presentation for*A*@¥,, is established with m*generators*and (n* + Sn —4)/2*relations*. ...##
###
Finite Diagram Semigroups: Extending the Computational Horizon
[article]

2015
*
arXiv
*
pre-print

Here we describe diagram

arXiv:1502.07150v2
fatcat:3equo33pszf6nnalsmnixnb55i
*semigroups*in*a**general*framework and extend our computational knowledge*of*them. ...*The**generated*data*set*is replete with surprising observations raising many open questions for further theoretical research. ...*The*conceptual origin*of*diagram*semigroups*is*the*notion*of*binary*relation**on**a**set**A*. ...##
###
Page 2474 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

*The*purpose

*of*this paper is to determine all maximal regular subsemigroups

*of*all ideals

*of*7,,,

*the*

*full*

*transformation*semi- group

*on*

*a*finite

*set*¥ = X, = {1,2,... ...

*The*results

*related*to special classes

*of*

*semigroup*elements (idempotents, nilpotents) are discussed, with

*a*focus

*on*questions associated with

*the*form

*of*

*transformation*

*semigroups*

*generated*by these ...

##
###
Page 555 of Mathematical Reviews Vol. , Issue 82b
[page]

1982
*
Mathematical Reviews
*

Soc. 41
(1966), 707-716; MR 36 #2728]

*on**the*idempotent-*generated*subsemigroup*of**the**full**transformation**semigroup*(X)*of**a**set*X, by obtaining some elegant arithmetic results. ... This is then applied to show that for any*set*X,*the**semigroup**of*all almost identical*full**transformations*and*the**semigroup**of*all almost identical*one*-to-*one*partial*transformations**on*X are factorizable ...##
###
Page 6078 of Mathematical Reviews Vol. , Issue 2004h
[page]

2004
*
Mathematical Reviews
*

Algebra 26 (1998), no. 3, 733-748; MR 99b:20099],

*the*first two and*the*last authors investigated relative ranks*of**the**semigroup*7y*of**full**transformations**on**a**set*XY. ...*The*rank*of**a**semigroup*S is*the*minimum cardinality*of**a**set*that*generates*S. For*a*subset*A**of*S,*the*relative rank*of*S modulo*A*is*the*minimum cardinality*of**a**set*B such that*A*U B*generates*S. ...##
###
Sonlu zincir üzerindeki tam daralma dönüşümlerinin bazı alt yarıgruplarının rankları

2020
*
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
*

Let + denotes

doi:10.25092/baunfbed.707344
fatcat:aju6pfk6nffsplhj5smu4eqagi
*the**set**of*all positive integers. Let = {1,2, ... , } be*the*finite chain for ∈ + and let be*the**full**transformation**semigroup**on*. ... Also let and be*the**semigroup**of*order-preserving*full*contraction mappings, and*the**semigroup**of*order-preserving or order-reversing*full*contraction mappings*on*, respectively. ... Acknowledgement We would like to thank*the*referees for their valuable comments which helped to improve*the*manuscript. ...
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