Idempotent and nilpotent elements in octonion rings over Z-Reference-Cited by-同舟云学术

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Idempotent and nilpotent elements in octonion rings over Z

Published:2024-03-15 Issue:1 Volume:69 Page:3-14
ISSN:0252-1938
Container-title:Studia Universitatis Babes-Bolyai Matematica
language:
Short-container-title:Stud. Univ. Babes-Bolyai Math.

Author:

,Aristidou Michael^ORCID,Brown Philip R.^ORCID, ,Chailos George^ORCID,

Abstract

In this paper, we show that the set O/Zp, where p is a prime number, does not form a skew field and discuss idempotent and nilpotent elements in the (finite) ring O/Zp. We provide examples and establish conditions for idempotency and nilpotency. Mathematics Subject Classification (2010): 15A33, 15A30, 20H25, 15A03. Received 27 July 2021; Accepted 14 December 2021

Publisher

Babes-Bolyai University Cluj-Napoca

Reference28 articles.

1. "1. Ankeny, N.C., Sum of three squares, Proc. Amer. Math. Soc., 8(2)(1957), 316-319.

2. 2. Aristidou, M., Demetre, A., A note on quaternion rings over Zp, Int. J. Alg., 3(15)(2009), 725-728.

3. 3. Aristidou, M., Demetre, A., Idempotent elements in quaternion rings over Zp, Int. J. Alg., 6(5)(2012), 249-254.

4. 4. Aristidou, M., Demetre, A., Nilpotent elements in quaternion rings over Zp, Int. J. Alg., 6(14)(2012), 663-666.

5. 5. Ayoub, R., Ayoub, C., On the commutativity of rings, Am. Math. Mon., 71(3)(1964), 267-271.

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