International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 671401, 13 pages
doi:10.1155/2010/671401
Research Article
Brandt Extensions and Primitive Topological Inverse Semigroups
1Department of Math/CSC, Saint Joseph's University, 5600 City Avenue, Philadelphia, PA 19131, USA
2Department of Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv 79000, Ukraine
3Pidstrygach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences, Naukova 3b, Lviv 79060, Ukraine
Received 20 July 2009; Accepted 1 February 2010
Academic Editor: Volker Runde
Copyright © 2010 Tetyana Berezovski et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- C. Eberhart and J. Selden, “On the closure of the bicyclic semigroup,” Transactions of the American Mathematical Society, vol. 144, pp. 115–126, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. H. Carruth, J. A. Hildebrant, and R. J. Koch, The Theory of Topological Semigroups, vol. 75 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1983. View at MathSciNet
- J. H. Carruth, J. A. Hildebrant, and R. J. Koch, The Theory of Topological Semigroups. Vol 2, vol. 100 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1986. View at MathSciNet
- A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Vol. I, Mathematical Surveys, no. 7, American Mathematical Society, Providence, RI, USA, 1961. View at MathSciNet
- A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Vol. II, Mathematical Surveys, no. 7, American Mathematical Society, Providence, RI, USA, 1967. View at MathSciNet
- R. Engelking, General Topology, vol. 6 of Sigma Series in Pure Mathematics, Heldermann, Berlin, Germany, 2nd edition, 1989. View at MathSciNet
- J. M. Howie, Fundamentals of Semigroup Theory, vol. 12 of London Mathematical Society Monographs, Clarendon Press, Oxford, UK, 1995. View at MathSciNet
- M. Petrich, Inverse Semigroups, Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1984. View at MathSciNet
- O. V. Gutik and K. P. Pavlyk, “-closed topological semigroups and Brandt -extensions,” Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, vol. 44, no. 3, pp. 20–28, 2001 (Ukrainian). View at MathSciNet
- O. V. Gutik and K. P. Pavlyk, “On Brandt -extensions of semigroups with zero,” Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, vol. 49, no. 3, pp. 26–40, 2006. View at MathSciNet
- J. A. Green, “On the structure of semigroups,” Annals of Mathematics, vol. 54, pp. 163–172, 1951. View at Zentralblatt MATH · View at MathSciNet
- J. W. Stepp, “A note on maximal locally compact semigroups,” Proceedings of the American Mathematical Society, vol. 20, no. 1, pp. 251–253, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- O. Gutik and K. Pavlyk, “Topological Brandt -extensions of absolutely -closed topological inverse semigroups,” Visnyk of the Lviv University. Series Mechanical and Mathematical, vol. 61, pp. 98–105, 2003.
- J. W. Stepp, “Algebraic maximal semilattices,” Pacific Journal of Mathematics, vol. 58, no. 1, pp. 243–248, 1975. View at Zentralblatt MATH · View at MathSciNet
- O. Gutik and D. Repovš, “On Brandt -extensions of monoids with zero,” Semigroup Forum, vol. 80, no. 1, pp. 8–32, 2010. View at Publisher · View at Google Scholar
- O. Gutik, K. Pavlyk, and A. Reiter, “Topological semigroups of matrix units and countably compact Brandt -extensions,” Matematychni Studii, vol. 32, no. 2, pp. 115–131, 2009.
- K. P. Pavlyk, “Absolutely -closed topological semigroups and Brandt -extensions,” Applied Problems of Mechanics and Mathematics, vol. 2, pp. 61–68, 2004 (Ukrainian).
- E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, vol. 1, Springer, Berlin, Germany, 1963.
- O. Gutik and D. Repovš, “On countably compact 0-simple topological inverse semigroups,” Semigroup Forum, vol. 75, no. 2, pp. 464–469, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- K. P. Pavlyk, Topological semigroups of matrix units and Brandt λ-extensions of topological semigroups, Ph.D. thesis, Lviv University (Ukrainian), 2006.
- W. W. Comfort and K. A. Ross, “Pseudocompactness and uniform continuity in topological groups,” Pacific Journal of Mathematics, vol. 16, pp. 483–496, 1966. View at Zentralblatt MATH · View at MathSciNet
- A. D. Aleksandrov, “On an extension of Hausdorff space to -closed,” Doklady Akademii Nauk SSSR, vol. 37, pp. 138–141, 1942 (Russian). View at Zentralblatt MATH
- D. Raikov, “On the completion of topological groups,” Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, vol. 10, pp. 513–528, 1946 (Russian). View at Zentralblatt MATH · View at MathSciNet
- D. N. Dikranjan and V. V. Uspenskij, “Categorically compact topological groups,” Journal of Pure and Applied Algebra, vol. 126, no. 1–3, pp. 149–168, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet