Tripotent elements in quaternion rings over ℤp

Author:

Aristidou Michael1,Hailemariam Kidus2

Affiliation:

1. Texas A&M University at Galveston , Galveston TX

2. Independent Researcher , Bloomington MN

Abstract

Abstract In this paper, we discuss tripotent1 elements in the finite ring ℍ/ℤp. We provide examples and establish conditions for tripotency. We follow similar methods used in [3] for idempotent elements in ℍ/ℤp.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference14 articles.

1. [1] N. C. Ankeny, Sum of Three Squares, Proc. Amer. Math. Soc., 8 (2) (1957), 316–319.

2. [2] M. Aristidou and A. Demetre, A Note on Quaternion Rings over ℤp, Int. J. Algebra, 3 (15) (2009), 725–728.

3. [3] M. Aristidou and A. Demetre, Idempotent Elements in Quaternion Rings over ℤp, Int. J. Algebra, 6 (5) (2012), 249–254.

4. [4] P. Damianou, Commutative Rings (in Greek), Proceedings of the 9th Cyprus Conference of Mathematics Education and Science, Cyprus, 2007, 165–166.

5. [5] I. N. Herstein, Topics in Algebra, 2nd ed., Wiley, NY, 1975.

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1. Tripotent Divisor Graph of a Commutative Ring;International Journal of Mathematics and Mathematical Sciences;2024-01

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