The order of the second group of units of the ring Z[i]/ < β >

Wiam M. Zeid

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 $\phi (n)$.

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How to Cite this Article

Wiam M. Zeid, The order of the second group of units of the ring Z[i]/ < β >, J. Math. Comput. Sci., 7 (2017), 30-38

Copyright © 2017 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.