It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we will characterize Ne-Noetherian rings and U-Noetherian rings by Ne-inject...It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we will characterize Ne-Noetherian rings and U-Noetherian rings by Ne-injective modules and U-injective modules.展开更多
A ring R is said to be right U-Noetherian if R satisfies ascending chain condition （ACC） on uniform right ideals. This article characterizes U-Noetherian ring by U-injective modules and discusses the extensions of U...A ring R is said to be right U-Noetherian if R satisfies ascending chain condition （ACC） on uniform right ideals. This article characterizes U-Noetherian ring by U-injective modules and discusses the extensions of U-Noetherian ring.展开更多
基金the National Natural Science Foundation of China(10171082)
文摘It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we will characterize Ne-Noetherian rings and U-Noetherian rings by Ne-injective modules and U-injective modules.
基金Supported by the Scientific Research Foundation of Gansu Provincial Education Department (0813B-01)
文摘A ring R is said to be right U-Noetherian if R satisfies ascending chain condition （ACC） on uniform right ideals. This article characterizes U-Noetherian ring by U-injective modules and discusses the extensions of U-Noetherian ring.
