Prime Modules
1965 ◽
Vol 17
◽
pp. 1041-1052
◽
Keyword(s):
Characterizations for prime and semi-prime rings satisfying the right quotient conditions (see § 1) have been determined by A. W. Goldie in (4 and 5). A ring R is prime if and only if the right annihilator of every non-zero right ideal is zero. A natural generalization leads one to consider right R-modules having the properties that the annihilator in R of every non-zero submodule is zero and regular elements in R annihilate no non-zero elements of the module. This is the motivation for the definition of prime module in § 1.