Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Primitive elements of Galois extensions of finite fields


Authors: Isao Kikumasa and Takasi Nagahara
Journal: Proc. Amer. Math. Soc. 115 (1992), 593-600
MSC: Primary 12E20; Secondary 11T99, 12E12, 13B05
MathSciNet review: 1081697
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: As is well known, $ {N_q}(n) = (1/n)\sum\nolimits_{d\vert n} {\mu (d){q^{n/d}}} $ coincides with the number of monic irreducible polynomials of $ \operatorname{GF}(q)[X]$ of degree $ n$. In this note we discuss the curve $ _n{{\text{N}}_X}(n)$ and the solutions of equations $ _n{{\text{N}}_X}(n) = b(b \geq n)$. As a corollary of these results, we present a necessary and sufficient arithmetical condition for $ R/K$ to have a primitive element.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12E20, 11T99, 12E12, 13B05

Retrieve articles in all journals with MSC: 12E20, 11T99, 12E12, 13B05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1081697-8
PII: S 0002-9939(1992)1081697-8
Article copyright: © Copyright 1992 American Mathematical Society