Noncommutative Generalizations of Theorems of Cohen and Kaplansky
Noncommutative Generalizations of Theorems of Cohen and Kaplansky
This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp. principal) iff every "prime right ideal" is finitely generated (resp. principal), …