2023/06/10 by O. V. Lyubimtsev, Lyubimtsev, Oleg, A. A. Tuganbaev +1
Mathematics · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2306.06445
Let R be a ring and let J(R), C(R) be its Jacobson radical and center, correspondingly. If R is a centrally essential ring and the factor ring R/J(R) is commutative, then any minimal right ideal is contained in the center C(R). A right Artinian (or right Noetherian subdirectly indecomposable) centrally essential ring is a right and left Artinian local ring. We describe centrally essential Noetherian subdirectly indecomposable rings and centrally essential rings with subdirectly indecomposable center. We give examples of non-commutative subdirectly indecomposable, centrally essential rings. The work of Oleg Lyubimtsev is supported by Ministry of Education and Science of the Russian Federation, project FSWR-2023-0034. The study of Askar Tuganbaev is supported by grant of Russian Science Foundation (=RSF), project 22-11-00052, https://rscf.ru/en/project/22-11-00052.