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- W1969904018 abstract "Let R be a commutative ring with identity and M be a finitely generated perfect R -module of homological dimension n with a projective resolution F :0→F n → f n f n−1 →·→F k → f k F k−1 →·→F 1 → 1 F 0 →M→0 where rank f k is r k . In this paper, we show that for 1< k < n , the ideals I r −1 ( f k ), I r −1 ( f k ) and I ( f k ) have the same radical as the annihilator of M , provided either n is even or M is Gorenstein and n ≡1mod4. Thus we show that the rank of the k th syzygy of M , r k ≥3, for 1< k < Pd ( M ) if the module M is perfect of even homological dimension or Gorenstein and Pd( M )≡1mod4." @default.
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- W1969904018 date "1990-07-01" @default.
- W1969904018 modified "2023-10-18" @default.
- W1969904018 title "Ranks of syzygies of perfect modules" @default.
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- W1969904018 doi "https://doi.org/10.1016/0022-4049(90)90102-n" @default.
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