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### On a set of generating relations of the full transformation semigroups

Nagayoshi Iwahori, Nobuko Iwahori
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

R. Kehinde, O. H. Abdulazeez
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

Peter Gallagher, Nik Ruškuc
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

Vítor H. Fernandes
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  .  ...  ] full transformations on a finite chain.  ...  full transformations on a finite chain.  ...

### Ranks of Identity Difference Transformation Semigroup

Omelebele Jude. A., Udoaka O. G., Udoakpan I. U.
2022 International journal of pure mathematics
This study focuses 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]

James East, Attila Egri-Nagy, Andrew R. Francis, James D. Mitchell
2015 arXiv   pre-print
Here we describe diagram 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

Kemal TOKER
2020 Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Let + denotes 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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