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A NOTE ON BILATERAL SEMIDIRECT PRODUCT DECOMPOSITIONS OF SOME MONOIDS OF ORDER-PRESERVING PARTIAL PERMUTATIONS
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 Title & Authors
A NOTE ON BILATERAL SEMIDIRECT PRODUCT DECOMPOSITIONS OF SOME MONOIDS OF ORDER-PRESERVING PARTIAL PERMUTATIONS
Fernandes, Vitor H.; Quinteiro, Teresa M.;
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 Abstract
In this note we consider the monoid of all monotone partial permutations on and its submonoids , and of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids and are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that is a quotient of a semidirect product of and the group of order two and, analogously, is a quotient of a semidirect product of and .
 Keywords
transformations;partial isometries;order-preserving;semidirect products;pseudovarieties;
 Language
English
 Cited by
 References
1.
A. Ya. Aizenstat, The defining relations of the endomorphism semigroup of a finite linearly ordered set, Sibirsk. Mat. Z. 3 (1962), 161-169 (Russian).

2.
F. Al-Kharousi, R. Kehinde, and A. Umar, Combinatorial results for certain semigroups of partial isometries of a finite chain, Australas. J. Combin. 58 (2014), no. 3, 365-375.

3.
F. Al-Kharousi, R. Kehinde, and A. Umar, On the semigroup of partial isometries of a finite chain, Communications in Algebra. To appear.

4.
C. J. Ash, Finite semigroups with commuting idempotents, J. Austral. Math. Soc. Ser. A 43 (1987), no. 1, 81-90. crossref(new window)

5.
D. F. Cowan and N. R. Reilly, Partial cross-sections of symmetric inverse semigroups, Int. J. Algebra Comput. 5 (1995), no. 3, 259-287. crossref(new window)

6.
M. Delgado and V. H. Fernandes, Abelian kernels of some monoids of injective partial transformations and an application, Semigroup Forum 61 (2000), no. 3, 435-452. crossref(new window)

7.
M. Delgado and V. H. Fernandes, Abelian kernels of monoids of order-preserving maps and of some of its exten-sions, Semigroup Forum 68 (2004), no. 3, 335-356. crossref(new window)

8.
V. D. Derech, Quasi-orders over certain inverse semigroups, Soviet Math. 35 (1991), no. 3, 74-76; translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1991 (1991), no. 3, 76-78.

9.
V. H. Fernandes, Semigroups of order-preserving mappings on a finite chain: a new class of divisors, Semigroup Forum 54 (1997), no. 2, 230-236. crossref(new window)

10.
V. H. Fernandes, Normally ordered inverse semigoups, Semigroup Forum 58 (1998), no. 3, 418-433.

11.
V. H. Fernandes, The monoid of all injective order preserving partial transformations on a finite chain, Semigroup Forum 62 (2001), no. 2, 178-204. crossref(new window)

12.
V. H. Fernandes, A new class of divisors of semigroups of isotone mappings of finite chains, Izv. Vyssh. Uchebn. Zaved. Mat. 2002 (2000), no. 3, 51-59; translation in Russian Math. (Iz. VUZ) 46 (2002), no. 3, 47-55.

13.
V. H. Fernandes, Normally ordered semigroups, Glasg. Math. J. 50 (2008), no. 2, 325-333.

14.
V. H. Fernandes, G. M. S. Gomes, and M. M. Jesus, Presentations for some monoids of injective partial transformations on a finite chain, Southeast Asian Bull. Math. 28 (2004), no. 5, 903-918.

15.
V. H. Fernandes and T. M. Quinteiro, Bilateral semidirect product decompositions of transformation monoids, Semigroup Forum 82 (2011), no. 2, 171-187.

16.
V. H. Fernandes and T. M. Quinteiro, On the monoids of transformations that preserve the order and a uniform partition, Comm. Algebra 39 (2011), no. 8, 2798-2815. crossref(new window)

17.
V. H. Fernandes and T. M. Quinteiro, Presentations for monoids of finite partial isometries, Semigroup Forum, DOI 10.1007/s00233-015-9759-4. To appear. crossref(new window)

18.
V. H. Fernandes and M. V. Volkov, On divisors of semigroups of order-preserving map-pings of a finite chain, Semigroup Forum 81 (2010), no. 3, 551-554. crossref(new window)

19.
O. Ganyushkin and V. Mazorchuk, On the structure of $IO_n$, Semigroup Forum 66 (2003), no. 3, 455-483. crossref(new window)

20.
G. M. S. Gomes and J. M. Howie, On the ranks of certain semigroups of order-preserving transformations, Semigroup Forum 45 (1992), no. 3, 272-282. crossref(new window)

21.
P. M. Higgins, Divisors of semigroups of order-preserving mappings on a finite chain, Internat. J. Algebra Comput. 5 (1995), no. 6, 725-742. crossref(new window)

22.
P. M. Higgins, Pseudovarieties generated by classes of transformation semigroups, Proc. St. Petersburg Semigroup Conference Russian State Hydrometeorological Inst., 85-94, 1999.

23.
J. M. Howie, Product of idempotents in certain semigroups of transformations, Proc. Edinburgh Math. Soc. 17 (1971), 223-236. crossref(new window)

24.
J. M. Howie, Fundamentals of Semigroup Theory, Oxford, Oxford University Press, 1995.

25.
M. Kunze, Zappa products, Acta Math. Hungar. 41 (1983), no. 3-4, 225-239. crossref(new window)

26.
M. Kunze, Lineare Parallelrechner I, Elektron. Informationsverarb. Kybernet. 20 (1984),no. 1, 9-39 (German).

27.
M. Kunze, Lineare Parallelrechner II, Elektron. Informationsverarb. Kybernet. 20 (1984),no. 2-3, 111-147 (German).

28.
M. Kunze, Bilateral semidirect products of transformation semigroups, Semigroup Forum 45 (1992), no. 2, 166-182. crossref(new window)

29.
M. Kunze, Standard automata and semidirect products of transformation semigroups, The-oret. Comput. Sci. 108 (1993), no. 1, 151-171.

30.
A. Laradji and A. Umar, Combinatorial results for semigroups of order-preserving par-tial transformations, J. Algebra 278 (2004), no. 1, 342-359. crossref(new window)

31.
A. Laradji and A. Umar, Combinatorial results for semigroups of order-preserving full transformations, Semigroup Forum 72 (2006), no. 1, 51-62. crossref(new window)

32.
T. G. Lavers, Presentations of general products of monoids, J. Algebra 204 (1998), no.2, 733-741. crossref(new window)

33.
J.-E. Pin, Varieties of Formal Languages, Plenum, London, 1986.

34.
L. M. Popova, The defining relations of the semigroup of partial endomorphisms of a finite linearly ordered set, Leningradskij gosudarstvennyj pedagogicheskij institut imeni A. I. Gerzena, Uchenye Zapiski 238 (1962), 78-88 (Russian).

35.
J. Rhodes and B. Tilson, The kernel of monoid morphisms, J. Pure Appl. Algebra 62(1989), no. 3, 227-268. crossref(new window)

36.
A. S. Vernitskii and M. V. Volkov, A proof and generalisation of Higgins' division the-orem for semigroups of order-preserving mappings, Izvestiya VUZ. Matematika (1995),no. 1, 38-44. (Russian); English translation in: Russ. Math. Izv. VUZ 39 (1995), no. 134-39.