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Paper   IPM / M / 15323
School of Mathematics
  Title:   Torsion-free aluffi algebras
  Author(s):  Abbas Nasrollah Nejad (Joint with Z. Shahidi and R. Zaare-Nahandi)
  Status:   Published
  Journal: J. Algebra
  Vol.:  513
  Year:  2018
  Pages:   190-207
  Supported by:  IPM
A pair of ideals JIR has been called Aluffi torsion-free if the Aluffi algebra of I/J is isomorphic with the corresponding Rees algebra. We give necessary and sufficient conditions for the Aluffi torsion-free property in terms of the first syzygy module of the form ideal J* in the associated graded ring of I. For two pairs of ideals J1,J2I such that J1J2I2, we prove that if one pair is Aluffi torsion-free the other one is so if and only if the first syzygy modules of J1 and J2 have the same form ideals. We introduce the notion of strongly Aluffi torsion-free ideals and present some results on these ideals.

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