Bi-amalgamations of commutative feebly clean-like rings

We investigate the transfer of the notion of feebly clean along with related concepts such as feebly [Formula: see text]-clean, and feebly nil-clean rings, to bi-amalgamated algebras along ideals. For example, we prove that the ring [Formula: see text] is feebly clean ([Formula: see text]-clean, nil-clean) under the conditions [Formula: see text], and one of the rings [Formula: see text], [Formula: see text], and [Formula: see text] is feebly clean ([Formula: see text]-clean, nil-clean). Also, we provide new characterizations of feebly [Formula: see text]-clean and feebly clean rings. All along the paper, we use the results to build examples subject to the mentioned concepts.

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Publication Details

Journal
Journal of Algebra and Its Applications
Published
2025-02-13
DOI
https://doi.org/10.1142/s0219498826501653
Primary Topic
Rings, Modules, and Algebras
Type
article
Field-Weighted Citation Impact
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article

Bi-amalgamations of commutative feebly clean-like rings

Mohammad Adarbeh, Khalid Adarbeh
Journal of Algebra and Its Applications
Rings, Modules, and Algebras
article

Bi-amalgamations of commutative feebly clean-like rings

Mohammad Adarbeh, Khalid Adarbeh
article en

Abstract

We investigate the transfer of the notion of feebly clean along with related concepts such as feebly [Formula: see text]-clean, and feebly nil-clean rings, to bi-amalgamated algebras along ideals. For example, we prove that the ring [Formula: see text] is feebly clean ([Formula: see text]-clean, nil-clean) under the conditions [Formula: see text], and one of the rings [Formula: see text], [Formula: see text], and [Formula: see text] is feebly clean ([Formula: see text]-clean, nil-clean). Also, we provide new characterizations of feebly [Formula: see text]-clean and feebly clean rings. All along the paper, we use the results to build examples subject to the mentioned concepts.

Journal of Algebra and Its Applications
An-Najah National University (PS), Birzeit University (PS)
Openalex Percentile: Top 95%
Rings, Modules, and Algebras
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