Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T18:22:18.073Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Semisimple Loop Algebras of Indecomposable RA Loops

Published online by Cambridge University Press:  20 November 2018

Swati Sidana  and
R. K. Sharma
Swati Sidana
Affiliation:
Department Of Mathematics, Indian Institute of Technology Delhi, New Delhi, India. R. K. Sharma is the corresponding author e-mail: [email protected] e-mail: [email protected]
R. K. Sharma
Affiliation:
Department Of Mathematics, Indian Institute of Technology Delhi, New Delhi, India. R. K. Sharma is the corresponding author e-mail: [email protected] e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

There are seven classes of finite indecomposable RA loops upto isomorphism. In this paper, we completely characterize the structure of the unit loop of loop algebras of these seven classes of loops over finite fields of characteristic greater than 2.

Keywords

20N0517D05unit looploop algebraindecomposable RA loops
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 2 , 01 June 2015 , pp. 363 - 373
Copyright
Copyright © Canadian Mathematical Society 2015

References

[1] Ferraz, R. A., Goodaire, E. G., and Milies, C. P., Some classes of semisimple group (and loop) algebras over finite fields. J. Algebra 324 (2010), 3457–3469. http://dx.doi.Org/10.1016/j.jalgebra.2O10.O9.OO5 Google Scholar
[2] Goodaire, E. G., Six Moufang loops of units. Canad. J. Math. 44 (1992), 951–973. http://dx.doi.org/10.4153/CJM-1992-059-7 Google Scholar
[3] Goodaire, E. G., Jespers, E., and Milies, C. P., Alternative loop rings. North-Holland Math. Stud. 184, Elsevier, Amsterdam, 1996.Google Scholar
[4] Jespers, E. and Leal, G., A characterization of the unit loop of the integral loop ringZMig(Q, 2). J. Algebra 155 (1993), 95–109. http://dx.doi.org/10.1006/jabr.1993.1032 Google Scholar
[5] Jespers, E., Leal, G., and Milies, C. P., Classifying indecomposable RA loops. J. Algebra 176 (1995), 569–584. http://dx.doi.Org/10.1006/jabr.1995.1260 Google Scholar
[6] Lidl, R. and Niederreiter, H., Introduction to finite fields and applications. Cambridge University Press, Cambridge, 1994.Google Scholar
[7] Milies, C. P. and Sehgal, S. K., An introduction to group rings. Vol. 1, Kluwer Academic Publishers, Dordrecht, 2002.Google Scholar
[8] Sidana, S. and Sharma, R. K., The unit loop of finite loop algebras of loops of order 32. Beitr. Algebra Geom. 56 (2015), no. 1, 339–349. http://dx.doi.Org/10.1007/s13366-013-0166-2 Google Scholar
[9] Sidana, S. and Sharma, R. K., Finite loop algebras o/RA loops of order 64. Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 30 (2014), no. 1, 27–42.Google Scholar
[10] Zhevlakov, K. A., Slin'ko, A. M., Shestakov, I. P., and Shirshov, A. I., Rings that are nearly associative. Vol. 104, Academic Press, New York-London, 1982. Translated by Harry E Smith.Google Scholar