INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS

Singha, Boorapa; Sanwong, Jintana; Sullivan, Robert Patrick

doi:10.4134/BKMS.2012.49.1.109

HOME > Journal Browse > About Journal > Journal Vol & Issue > Full Record

INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS

Journal title : Bulletin of the Korean Mathematical Society
Volume 49, Issue 1, 2012, pp.109-126
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2012.49.1.109

Title & Authors

INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS
Singha, Boorapa; Sanwong, Jintana; Sullivan, Robert Patrick;

Abstract

In 2003, Marques-Smith and Sullivan described the join ${${\Omega}$}$ of the `natural order` ${$\leq$}$ and the `containment order` ${$\subseteq$}$ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective ${${\alpha}{\in}P(X)$}$ such that ${\mid}X{\backslash}X{\alpha}\mid

Keywords

partial transformation semigroup;Baer-Levi semigroup;inverse semigroup;natural order;containment order;meet and join;

Language

English

Cited by

References

S. Y. Chen and S. C. Hsieh, Factorizable inverse semigroups, Semigroup Forum 8 (1974), no. 4, 283-297.

A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Mathematical Surveys, No. 7, vol 1 and 2, American Mathematical Society, Providence, RI, 1961 and 1967.

J. M. Howie, An Introduction to Semigroup Theory, Academic Press, London, 1976.

J. M. Howie, A congruence-free inverse semigroup associated with a pair of innite cardinals, J. Aust. Math. Soc. 31 (1981), no. 3, 337-342.

G. Kowol and H. Mitsch, Naturally ordered transformation semigroups, Monatsh. Math. 102 (1986), no. 2, 115-138.

I. Levi, Automorphisms of normal partial transformation semigroups, Glasg. Math. J. 29 (1987), no. 2, 149-157.

M. P. O. Marques-Smith and R. P. Sullivan, Partial orders on transformation semigroups, Monatsh. Math. 140 (2003), no. 2, 103-118.

H. Mitsch, A natural partial order for semigroups, Proc. Amer. Math. Soc. 97 (1986), no. 3, 384-388

F. A. Pinto and R. P. Sullivan, Baer-Levi semigroups of partial transformations, Bull. Aust. Math. Soc. 69 (2004), no. 1, 87-106.

10.

J. Sanwong and R. P. Sullivan, Injective transformations with equal gap and defect, Bull. Aust. Math. Soc. 79 (2009), no. 2, 327-336.

11.

B. Singha, J. Sanwong, and R. P. Sullivan, Partial orders on partial Baer-Levi semigroups, Bull. Aust. Math. Soc. 81 (2010), no. 2, 195-207.

12.

R. P. Sullivan, Automorphisms of transformation semigroups, J. Aust. Math. Soc. 20 (1975), 77-84.

13.

R. P. Sullivan, Semigroups generated by nilpotent transformations, J. Algebra 110 (1987), no. 2, 324-343.

14.

R. P. Sullivan, Partial orders on linear transformation semigroups, Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), no. 2, 413-437.