On clean, weakly clean and feebly clean commutative group rings

A ring [Formula: see text] is said to be clean if each element of can written as the sum a unit and an idempotent. weakly either or difference idempotent, feebly every text], where are orthogonal idempotents. Clearly, rings both them clean. In recent paper (J. Algebra Appl. 17 (2018) 1850111 (5 pp.)), McGoven characterized when group clean, distinct primes. this paper, we consider more general setting. Let algebraic number field, its integers, nonzero prime ideal localization at text]. We investigate finite abelian group, establish explicit characterization for such case cyclotomic field quadratic field.