Extensions of Exchange Rings

✍ Scribed by Pere Ara

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 221 KB
• Volume: 197
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1997.7116

✦ Synopsis

We define non-unital exchange rings and we prove that if I is an ideal of a ring R, then R is an exchange ring if and only if I and RrI are exchange rings and idempotents can be lifted modulo I. We also show that we can replace the condition on liftability of idempotents with the condition that the canonical map Ž . Ž . K R ªK RrI be surjective.