Abstract
In this paper, we present an algorithmic method for computing a protective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this resolution to the study of the Ext-algebra of the algebra; namely, we present a new method for computing Yoneda products using the constructions of the resolutions. We also use our resolution to prove a case of the "no loop" conjecture.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2915-2939 |
| Number of pages | 25 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 353 |
| Issue number | 7 |
| DOIs | |
| State | Published - 2001 |
Keywords
- Finite dimensional and graded algebras
- Projective resolutions
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Cite this
Green, E. L., Solberg, & Zacharia, D. (2001). Minimal projective resolutions. Transactions of the American Mathematical Society, 353(7), 2915-2939. https://doi.org/10.1090/s0002-9947-01-02687-3