The order of the second group of units of the ring Z[i]/ < β >
Abstract
In this article we introduce a newely defined function $\phi _{G}^{2}(\beta )$ that represents the order of the second group of units of the ring $R=\mathbf{Z}[i]/<\beta >$. We examine some of the properties of this function that are similar to that of the Euler Phi function $\phi (n)$.
Copyright © 2016 Wiam M. Zeid. 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.
Cite this article
W. M. Zeid, The order of the second group of units of the ring Z[i]/ < β >, J. Math. Comput. Sci. 7 (2017), 30–38.
BibTeX
@article{Zeid2017,
author = {Zeid, Wiam M.},
title = {The order of the second group of units of the ring Z[i]/ < β >},
journal = {J. Math. Comput. Sci.},
volume = {7},
year = {2017},
pages = {30--38},
doi = {}
}