On a theorem of Anderson and Chun

DOI10.1216/rmj.2023.53.1zbMath1528.13002WikidataQ123183017 ScholiaQ123183017MaRDI QIDQ6158183

Farimah Farrokhpay, Ali Rezaie Aliabad, Mohammad Ali Siavoshi

Publication date: 31 May 2023

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-53/issue-1/ON-A-THEOREM-OF-ANDERSON-AND-CHUN/10.1216/rmj.2023.53.1.full

zbMATH Keywords

rings of continuous functionsregular range 1strongly regular associate

Mathematics Subject Classification ID

Algebraic properties of function spaces in general topology (54C40) Units, groups of units (associative rings and algebras) (16U60) Divisibility and factorizations in commutative rings (13A05)

Cites Work

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• Associate elements in commutative rings
• When is \(C(X)\) a clean ring?
• \(\Delta\)-rings
• Rings with internal cancellation.
• When are associates unit multiples?
• Cozero complemented spaces; when the space of minimal prime ideals of a \(C(X)\) is compact
• Stable rank of rings and dimensionality of topological spaces
• Annihilator-stability and unique generation
• GENERALIZATIONS OF COMPLEMENTED RINGS WITH APPLICATIONS TO RINGS OF FUNCTIONS
• Almost-P-Spaces
• Lifting Idempotents and Exchange Rings
• Clean Semiprimef-Rings with Bounded Inversion
• Study of Hopficity in Certain Classes of Rings
• Type conditions of stable range for identification of qualitative generalized classes of rings
• Annihilator-stability and unique generation in C(X)
• Uniqueness of Generators of Principal Ideals in Rings of Continuous Functions
• Elementary Divisors and Modules

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