Abstract
Let R be a commutative ring with identity. An element \(x\in R\) is said to be a clear element if it can be written as \(x=a+v\) where a is a unit-regular element, that is \(a=a^{2}u\) for some \(u\in U(R)\) and \(v\in U(R)\); and the ring itself is said to be a clear ring provided that every element is a clear element. In this paper we study the notions of clear rings in different contexts of commutative rings such us pullbacks, trivial ring extensions, amalgamations of algebras along ideals etc.
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The author would like to express his sincere thanks to both referees, their comments and corrections greatly improved this paper.
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Mimouni, A. Note on clear rings. Afr. Mat. 33, 49 (2022). https://doi.org/10.1007/s13370-022-00973-2
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DOI: https://doi.org/10.1007/s13370-022-00973-2