Disproof of Several Recently Published Results in Ring Theory

S K Pandey

doi:10.20944/preprints202310.0212.v3

Preprint Short Note Version 3 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 1 October 2023 / Approved: 4 October 2023 / Online: 4 October 2023 (05:28:47 CEST)
Version 2 : Received: 29 October 2023 / Approved: 30 October 2023 / Online: 1 November 2023 (02:37:41 CET)
Version 3 : Received: 3 November 2023 / Approved: 6 November 2023 / Online: 6 November 2023 (10:25:33 CET)

In this note we consolidate and give a brief description of several recently published results in ring theory having disproof. These results have been published during 2016 to 2021 in the so called non-predatory reputed mathematical journals indexed in the well known database like Scopus. We have considered results on rings in which each element is a sum of two idempotents appeared in Canad. Math. Bull. (2016), weakly tripotent rings appeared in Bull. Korean Math. Soc. (2018) and Rendiconti Sem. Mat. Univ. Pol. Torino (2021), involution t-clean rings appeared in Eur. J. Pure Appl. Math (2022) and strongly 2-nil clean rings with units of order two appeared in Eur. J. Pure Appl. Math (2023).

ring theory; algebra; mathematics; disproof; counterexamples; involution t-clean ring; weakly tripotent ring; invo-regular ring; locally invo-regular ring; strongly 2-nil clean ring; strongly nil clean ring

Computer Science and Mathematics, Algebra and Number Theory

Comment 1

Received: 6 November 2023
Commenter: S K Pandey
Commenter's Conflict of Interests: Author

Comment: Some more results have been included and the article has been revised.

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Disproof of Several Recently Published Results in Ring Theory

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