A Note on Quaternion Rings over Zp 1. Introduction

728 M. Aristidou and A. Demetre
”+”) turns H/Zn into a ring. We assume here that the author in [2] actually
intended the multiplication we provide above (as it is very close to ours), but
still that will not save Conjecture 2.1 (”Theorem 2” in [2]) from being false.
3. A counterexample for the case p = 3 was generously given to us by T. Dray,
in a recent PNW MAA Conference [CWU, Ellensburg, WA, 2009]. It goes as
follows: (1 + i − k)(1 + i + j) = 3i = 0 in H/Z3. We thank T. Dray for the
example.
Acknowledgment: We are grateful to M. Klassen for his comments on an
earlier draft and to T. Dray for the counterexample for the case p = 3, as well
as for other comments he made.
References
[1] I. N. Herstein Topics in Algebra, 2nd ed., Wiley, 1975.
[2] W. B. V. Kandasamy ”On Finite Quaternion Rings and Skew Fields”, Acta
Ciencia Indica, Vol.XXVI, No 2. p.133-135, 2000.
[3] R. S. Pierce Associative Algebras, Springer, 1982.
[4] R. Remmert et all Numbers, Springer, 1991.
[5] R. Schafer An Introduction to Nonassociative Algebras, Academic Press,
1996.
Received: March, 2009