… radical of a module as the dual notion of the prime radical. The second radical, sec ( M ) , of
a module … If R is a prime left bounded right and left Goldie ring which is not simple, we prove …

… prime submodule defined by F. Raggi et.al. we prove that the intersection of all prime submodules
of a Goldie module M… known fact that in a left Goldie ring, the prime radical is nilpotent. …

… In case M is a uniform module, then rad M is a prime ideal. … We shall require this
radical in order to study the question of the existence of basic modules. …

… of all prime submodules of M (note that, if M has no any prime … In Section 2, we study
the prime radical of Artinian modules. … prime left Goldie ring, and let M be a torsion-free R-module. …

… (2) to characterize prime and uniform prime modules. It is the … generalize Goldie's work on
semi-prime rings (3) to modules. … a radical for modules that is analogous to the prime radical of …

… R is fully left bounded left Goldie and the module M is finitely generated. It … radical submodule
N of a module M such that the factor module M/N has finite uniform dimension has a prime …

… of prime Goldie modules and the class of semiprime Goldie modules as generalizations of
prime right Goldie … Jenkin and PF Smith, On the prime radical of a module over a commutative …

… We show that over a left bounded prime left Goldie ring, the study of Baer–McCoy radicals
of general modules reduces to that of torsion modules. Moreover, over an FBN prime ring R …

… rings [3, 4] to modules. It is the aim of the present note to investigate these modules and
semi-prime Goldie … As in [2], an R-module M is said to be semi-prime if the prime radical P(M)" …

… -prime ring, that the nil radical N of A is nilpotent, that A satisfies the ascending chain condition
on right annihilators, and that both A and A IN are left Goldie … Q/N,-module. Hence QmQ is …