All right R-modules are I 0-modules if and only if either R is a right SV-ring or R/I (2) (R) is an Artinian serial ring such that the square of the Jacobson radical of R/I (2) (R) is equal to zero.A. N. AbyzovA. A. Tuganbaev...
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It is proved that all idempotents of a centrally essential alternative ring are central. Several examples of non-commutative centrally essential rings are provided, some properties of centrally essential rings are described.doi:10.1515/dma-2019-0019Viktor T. MarkovAskar A. Tuganbaev...
The fundamental result of the paper is Theorem I, asserting that over a right Noetherian ring R, the poor injectivity of all cyclic modules is equivalent to the fact that R is a direct sum of a semisimple Artinian ring and a finite number of uniserial rings and hereditary Noetherian...
A. Tuganbaev, “Rings over Which All Modules Are I 0 -Modules. II,” Fundament. i Prikl. Matem. 14 (2), 3–12 (2008).Rings over which all modules are I 0 -modules[J] . A. A. Tuganbaev.Journal of Mathematical Sciences . 2009 (2)...