2022/03/28 by Muhammad Zafrullah, Zafrullah, Muhammad
Mathematics · #13A18 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13A15 #Rings, Modules, and Algebras #Secondary 13G05
paper · pdf · doi:10.48550/arxiv.2203.14935
openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Professor Daniel Anderson informed me, recently, that there is an error in the proof of Theorem 56 of Kaplansky's book on Commutative Rings. His (Dan's) reason was "He (Kaplansky) orders by reverse inclusion but in the last line uses inclusion, so we don't contradict maximality (which is minimality)". The aim of this short note is to indicate that while Dan Anderson appears to be correct in pointing out an error in the proof of Theorem 56 of the above mentioned book, the statement of the theorem is a correct consequence of a Theorem of Chevalley.