自内射环的余Hopf性(英文)

CoHopficity of Self-Injective Rings

本文证明了自内射环 Ｒ是余 Ｈｏｐｆ的当且仅当 Ｒ满足 ｓｔａｂｌｅ ｒａｎｇｅ ｏｎｅ．于是得到了 Ｖａｒａｄａｒａｊａｎ在［９］中的公开问题对于自内射环是成立的，即 Ｍｎ（Ｒ）是余 Ｈｏｐｆ的当且仅当 Ｒ是余 Ｈｏｐｆ的，作为应用证明了 Ｇｏｏｄｅａｌ的一个公开问题对于自内射正则环有肯定的回答．

It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ring R. As a consequence of we answer problem of Goodeal in the affirmative in [3], for self-injective regular rings.