On \sum-nil-good rings
Moutu Abdou Salam Moutui\,^1
\,^{1} Department of Mathematics and Statistics St. Francis Xavier University Antigonish, Nova Scotia, Canada B2G 2W5.
Pages 168-175 | Received 30 June 2024, Accepted 22 January 2025, Published 26 January 2026
Abstract
In this paper, we introduce a new concept of ring called \sum-nil-good ring as a generalization of the notion of nil-good ring, in the context of commutative rings. We study some basic properties of this ring. We investigate this notion to various context of commutative ring extensions such as homomorphic image, direct product, power series ring and amalgamation ring, with application on the transfer of this property to trivial ring extension. Our goal is to generate a new original class of rings satisfying the above property.
Keywords: \sum-nil-good, nil-good, 2-nil-good, homomorphic image, direct product, amalgamation, trivial ring extension.
MSC numbers: Primary 13F05, 13A15, 13E05, 13F20, 13C10, 13C11, 13F30,
13D05.
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