Some Properties of Rings of the Type f(x),g(x)-clean
DOI:
https://doi.org/10.29304/jqcsm.2024.16.11445Keywords:
Matrix ring, g(x)-clean rings, f(x),g(x)-clean ringsAbstract
In [1], the authors introduced a property of rings called the f(x),g(x)-clean property. We investigate some new results about this property. In particular, we prove that the ring of matrices over a ring R is f(x),g(x)-clean if the ring R is f(x),g(x)-clean as well. We demonstrate, among many other things, that a ring's f(x),g(x)-cleanness may always be passed to R[[x]], but not always to its polynomial ring R[x].
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Copyright (c) 2024 Abdelwahab El Najjar, Akram S. Mohammed
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
