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Characterizations of the commutators involving idempotents in certain subrings of M2(Z)Özdİn, TufanGümüşel, GünseliClean (Nil-clean) elementcommutatoridempotentNilpotentunit elementunit-regular elementIn this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator [E1,E2] = E1E2 − E2E1 involving idempotents E1,E2 in certain subrings of M2(Z). © This work is licensed under a Creative Commons Attribution 4.0 International License.TUBITAK2023Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/12216https://doi.org/10.55730/1300-0098.34431300-0098enTurkish Journal of Mathematicsinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/12216