Strongly P-Clean and Semi-Boolean Group Rings

Bi-amalgamations subject to j-clean and weakly j-clean properties

“…, where Z (2) is the localization of Z at the prime ideal (2). Z (2) is J-clean by [23,Example 3.2] and hence A is also J-clean by [16,Example 2.19]. Now, consider the homomomorphism f :…”

“…As we mentioned in the introduction, nil clean rings are J-clean. The authors of [23] provided an example of a J-clean ring that is not nil clean [23,Remark 3.9]. Below, we use their example and Theorem 2.7 to enrich the literature with a new counterexample of a J-clean ring that is not nil clean, which is a fourth application of Theorem 2.7.…”