T-radicals in the category of modules. Acta Applicandae Mathematicae, 85 (2005)
Annotation
This paper investigates the properties of a special class of radicals de?ned
in the category of modules (T-radicals). In a sense the notion of a T-radical
synthesizes the de?nitions of an E-radical, appearing for the ?rst time in [4],
and a T-module [3].
The ?rst section is concerned with modules over some ring S, the second
one { both over the ring S and another ring R. It is suggested that R and S are
associative rings with unity, modules are unitary and, unless otherwise stated,
right. The category of right S-modules is designated mod-S. The word \group"
means the abelian group.
