Small Injective Rings

Liang Shen; Jianlong Chen

paper

Small Injective Rings

arXiv:math/0505445

Abstract

Let $R$ be a ring, a right ideal $I$ of $R$ is called small if for every proper right ideal $K$ of $R$ , $I + K \neq = R$ . A ring $R$ is called right small injective if every homomorphism from a small right ideal to $R_{R}$ can be extended to an $R$ -homomorphism from $R_{R}$ to $R_{R}$ . Properties of small injective rings are explored and several new characterizations are given for $QF$ rings and $P F$ rings, respectively.

14 pages

References in corpus (1)

A Note on Quasi-Frobenius Rings