Rings over which all modules are <Emphasis Type="Italic">I</Emphasis><Subscript>0</Subscript>-modules

Let A be a ring that does not contain an infinite set of idempotents that are orthogonal modulo the ideal SI(A _A ). It is proved that all A-modules are I ₀-modules if and only if either A is a right semi-Artinian, right V-ring or A/SI(A _A ) is an Artinian serial ring and the square of the Jacobson radical of A/SI(A _A ) isequal to zero. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 5, pp. 193–200, 2007.     

Plane modules and distributive rings

LetA be a semiprime ring entire over its center. We prove that the following conditions are equivalent: (a) A is a ring distributive from the right (left); (b) w.gl. dim (A) 1; moreover, ifM is an arbitrary prime ideal of the ringA, thenA/M is a right Ore set.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 721–724, May, 1993.     

Idempotent functors and localizations in categories of modules and Abelian groups

The present paper contains various results on idempotent functors and localizations in categories of modules and Abelian groups.