Acyclicity of Schur complexes and torsion freeness of Schur modules
Journal of Algebra, cilt.535, ss.133-158, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 535
- Basım Tarihi: 2019
- Doi Numarası: 10.1016/j.jalgebra.2019.05.035
- Dergi Adı: Journal of Algebra
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.133-158
- Anahtar Kelimeler: Schur complexes, Schur modules, Torsion freeness
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Hayır
Özet
Let R be a Noetherian commutative ring and M a R-module with pdRM≤1 that has rank. Necessary and sufficient conditions were provided in [1] for an exterior power ∧kM to be torsion free. When M is an ideal of R similar necessary and sufficient conditions were provided in [2] for a symmetric power SkM to be torsion free. We extend these results to a broad class of Schur modules Lλ/μM. En route, for any map of finite free R modules ϕ:F→G we also study the general structure of the Schur complexes Lλ/μϕ, and provide necessary and sufficient conditions for the acyclicity of any given Lλ/μϕ by computing explicitly the radicals of the ideals of maximal minors of all its differentials.