On 2-nil-clean commutative rings
Chahrazade Bakkari\,^1, Mohamed Es-Saidi\,^2 and Moutu Abdou Salam Moutui\,^3
\,^{1,2}Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Morocco
\,^{3}STEM Division, American University of Afghanistan, Doha Campus, Qatar
Pages 81-88 | Received 14 July 2024, Accepted 16 December 2024, Published 10 July 2025
Abstract
A ring R is said to be 2-nil-clean if any element in R can be written as the sum of two idempotents and a nilpotent [7]. In this paper, we exhibit the connections between this ring and other related classes of rings. Our specific aim is to illustrate how the 2-nil clean condition behaves with respect to several types of ring extensions such as polynomial ring, power series ring, amalgamated algebra and pullback. Our results produce new and original classes of 2-nil-clean rings subject to various ring theoretic properties.
Keywords: Amalgamated algebra, trivial ring extension, nil-clean ring, 2-nil-clean ring, weakly-nil-clean ring, pullback.
MSC numbers: 13F05, 13A15, 13E05, 13F20, 13C10, 13C11, 13F30, 13D05.
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