Hereditary Torsion Theory Counter Equivalences

✍ Scribed by R.R. Colby; K.R. Fuller

• Book ID: 102570400
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 177 KB
• Volume: 183
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0215

✦ Synopsis

Recently, we began to investigate this phenomenon as a further generalization of Morita equivalence, in particular Ž showing that such equivalences are induced by pairs of bimodules R. R. Colby and . K. R. Fuller, Comm. Algebra, 23 1995, 4833᎐4849 . Here we are concerned with conditions under which the torsion theories are hereditary. We begin with a characterization of the bimodules, and we apply it to determine just when one or both of the torsion theories are hereditary, to obtain examples, and to investigate global dimensions and Grothendieck groups of R and S. We assume the notation Ž and conventions of F. W. Anderson and K. R. Fuller 1992, ''Rings and Categories . Ž of Modules,'' 2nd ed., Springer-Verlag, New York and B. Stenstrom 1970, ''Rings .

of Quotients,'' Springer-Verlag, New YorkrHeidelbergrBerlin . In addition all ''subcategories'' are full subcategories of modules and all ''functors'' are additive functors.