Characterizations of the commutators involving idempotents in certain subrings of $M_{2}(\mathbb{Z})$

Authors: TUFAN ÖZDİN, GÜNSELİ GÜMÜŞEL

Abstract: In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]=E_1E_2-E_2E_1$ involving idempotents $E_1,E_2$ in certain subrings of $M_{2}(\mathbb{Z})$.

Keywords: Clean (Nil-clean) element, commutator, idempotent, unit element, Nilpotent, unit-regular element

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