Modules without Self-Extensions over Radical Cube Zero Rings

✍ Scribed by R. Schulz

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 156 KB
• Volume: 167
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1994.1177

✦ Synopsis

A conjecture of Tachikawa states that every finitely generated non-projective module (M) over a self-injective artinian ring (R) has a self-extension, i.e., (\operatorname{Ext}_{R}^{i}(M, M)) (\neq 0) for some (i \geqslant 1). We show that Tachikawa's conjecture holds for a class of radical cube zero rings. (C) 1994 Academic Press, Inc.