Research Article

THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS

Volume: 41 Number: 6 June 1, 2012
  • Nazmiye Alemdar
  • Osman Mucuk
EN TR

THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS

Abstract

In this paper we prove that the group structure of a group object in the category of groupoids lifts to a covering groupoid. We also prove similar results for a R-module object in the category of groupoids

Keywords

References

  1. Bateson, A. Fundamental groups of topological R-modules, Trans. Amer. Math. Soc. 270 (2), –536, 1982.
  2. Brown, R. Topology and groupoids, (BookSurge LLC, North Carolina, 2006).
  3. Brown, R. and Danesh-Naruie, G. The fundamental groupoid as a topological groupoid, Proc. Edinburgh Math. Soc. 19 (2), 237–244, 1975.
  4. Brown, R. and Mucuk, O. Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115, 97–110, 1994.
  5. Brown, R. and Spencer, C. B. G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Konn. Ned. Akad. v. Wet. 79, 296–302, 1976.
  6. Chevalley, C. Theory of Lie groups, (Princeton University Press, United States of America, ). Higgins, P. J. Notes on categories and groupoids (Van Nostrand Reinhold Company, Durham, England, 1971).
  7. Mucuk, O., Kılı¸carslan, B., S¸ahan, T. and Alemdar, N. Group-groupoid and monodromy groupoid, Topology Appl. 158, 2034–2042, 2011.
  8. Mucuk, O. Covering groups of non-connected topological groups and the monodromy groupoid of a topological groupoid(PhD Thesis, University of Wales, 1993).

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

Nazmiye Alemdar This is me

Osman Mucuk This is me

Publication Date

June 1, 2012

Submission Date

May 11, 2014

Acceptance Date

-

Published in Issue

Year 2012 Volume: 41 Number: 6

APA
Alemdar, N., & Mucuk, O. (2012). THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS. Hacettepe Journal of Mathematics and Statistics, 41(6), 813-822. https://izlik.org/JA64LN32HM
AMA
1.Alemdar N, Mucuk O. THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS. Hacettepe Journal of Mathematics and Statistics. 2012;41(6):813-822. https://izlik.org/JA64LN32HM
Chicago
Alemdar, Nazmiye, and Osman Mucuk. 2012. “THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS”. Hacettepe Journal of Mathematics and Statistics 41 (6): 813-22. https://izlik.org/JA64LN32HM.
EndNote
Alemdar N, Mucuk O (June 1, 2012) THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS. Hacettepe Journal of Mathematics and Statistics 41 6 813–822.
IEEE
[1]N. Alemdar and O. Mucuk, “THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 6, pp. 813–822, June 2012, [Online]. Available: https://izlik.org/JA64LN32HM
ISNAD
Alemdar, Nazmiye - Mucuk, Osman. “THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS”. Hacettepe Journal of Mathematics and Statistics 41/6 (June 1, 2012): 813-822. https://izlik.org/JA64LN32HM.
JAMA
1.Alemdar N, Mucuk O. THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS. Hacettepe Journal of Mathematics and Statistics. 2012;41:813–822.
MLA
Alemdar, Nazmiye, and Osman Mucuk. “THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 6, June 2012, pp. 813-22, https://izlik.org/JA64LN32HM.
Vancouver
1.Nazmiye Alemdar, Osman Mucuk. THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS. Hacettepe Journal of Mathematics and Statistics [Internet]. 2012 Jun. 1;41(6):813-22. Available from: https://izlik.org/JA64LN32HM