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Abstract
Rings in which the square of each unit is a sum of an idempotent and an element from the Jacobson radical are said to be 2-UJ. Properties of 2-UJ rings are discussed, and the 2-UJ property is applied to characterize some known notions of rings.
Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.
Acknowledgments
After the proofs were returned, the authors were made aware that the result in Theorem 3.3 is similar to result in Theorem 2.8 of Danchev, P. (2019). On exchange π-JU unital rings. Rendiconti Sem. Mat. Univ. Pol. Torino 77(1):13–23, although both the results are independent.
The authors are highly grateful to the anonymous referee for his/her insights and many valuable comments.
Additional information
Funding
This research was supported by the NNSF of China (no. 11401009) and the Key Project of Anhui Education Committee (no. gxyqZD2019009).