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Almost split sequences for relatively projective modules
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bautista, Raymundo Kleiner, M. K. |
| Copyright Year | 1990 |
| Abstract | The paper deals with almost split sequences. Introduced in [2] for the category mod A of finitely generated modules over an artin algebra A, almost split sequences were later found in the category of lattices over an order [l, 43, as well as in certain subcategories of mod A [6, l&3]. It is generally recognized that if almost split sequences exist, the subcategory has nice properties. We are concerned with the subcategory of relatively projective modules. Let R be a field or a Dedekind domain with the field of quotients k, and let A and A be finite-dimensional R-algebras or R-orders, respectively, with A mapped into A via an R-algebra map i: A -+ A. Here we understand orders and lattices in the sense of [ 1, p. 85, Example (b)]. Namely, A is an R-order if it is a noetherian R-algebra projective as an R-module, and x = k OR A is a self-injective ring. A-mod denotes the category of finitely generated left A-modules if R is a field, or the category of left A-lattices if R is a Dedekind domain, where a left A-module h4 is a lattice if it is a finitely generated projective R-module such that k Ox M is a projective |
| Starting Page | 19 |
| Ending Page | 56 |
| Page Count | 38 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/0021-8693(90)90148-H |
| Volume Number | 135 |
| Alternate Webpage(s) | https://core.ac.uk/download/pdf/82512805.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/0021-8693%2890%2990148-H |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
