Minimal projective resolutions
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- by E. L. Green, Ø. Solberg and D. Zacharia
- Trans. Amer. Math. Soc. 353 (2001), 2915-2939
- DOI: https://doi.org/10.1090/S0002-9947-01-02687-3
- Published electronically: March 8, 2001
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Abstract:
In this paper, we present an algorithmic method for computing a projective 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 $\operatorname {Ext}$-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.References
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Bibliographic Information
- E. L. Green
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
- MR Author ID: 76495
- ORCID: 0000-0003-0281-3489
- Email: green@math.vt.edu
- Ø. Solberg
- Affiliation: Institutt for matematiske fag, NTNU, Lade, N–7491 Trondheim, Norway
- Email: oyvinso@math.ntnu.no
- D. Zacharia
- Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
- MR Author ID: 186100
- Email: zacharia@mailbox.syr.edu
- Received by editor(s): September 21, 1998
- Received by editor(s) in revised form: January 3, 2000
- Published electronically: March 8, 2001
- Additional Notes: Partially supported by a grant from the NSA
Partially supported by NRF, the Norwegian Research Council - © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 2915-2939
- MSC (2000): Primary 16E05, 18G10; Secondary 16P10
- DOI: https://doi.org/10.1090/S0002-9947-01-02687-3
- MathSciNet review: 1828479
Dedicated: Dedicated to Helmut Lenzing for his 60th birthday