 Idempotent McCoy Rings and Their PropertiesAsma Ali, Amal S. Alali and Shafahat Hussain Journal of Mathematics, 2026, vol. 2026, 1-9 Abstract: This paper introduces idempotent McCoy rings, extending McCoy rings by incorporating idempotent elements, and explores their key properties. We provide examples and a counterexample showing that not every idempotent McCoy ring is McCoy. Our results show that if B is a Boolean ring, then the upper triangular matrix ring TnB is idempotent McCoy, but this does not hold for arbitrary rings R. Also, we show that idempotent McCoy property does not pass to its full matrix ring indicating the property is not Morita invariant. We prove that if TR,R is idempotent McCoy, so is R, with the converse holding when R is McCoy. The idempotent McCoy property is neither left–right symmetric nor included in abelian rings. Unlike McCoy rings, the quotient ring Rx/x2 is not idempotent McCoy. If Rx is idempotent McCoy, then R is also idempotent McCoy, though the converse may fail. Skew polynomial rings over idempotent McCoy rings may not inherit the property. We also prove that for a central idempotent e in R, R is idempotent McCoy if and only if both eR and 1−eR are idempotent McCoy. Finally, a relational diagram together with two tables is provided to summarize the similarities, differences, and relationships between McCoy and idempotent McCoy properties. Date: 2026 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7107628 DOI: 10.1155/jom/7107628 Access Statistics for this article More articles in Journal of Mathematics from Hindawi |
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