On the arithmetic and homology of algebras of linear type

Herzog, J.; Simis, A.; Vasconcelos, W. V.

doi:10.1090/S0002-9947-1984-0737891-6

On the arithmetic and homology of algebras of linear type
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by J. Herzog, A. Simis and W. V. Vasconcelos

Trans. Amer. Math. Soc. 283 (1984), 661-683

DOI: https://doi.org/10.1090/S0002-9947-1984-0737891-6

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Abstract:

Three modifications of the symmetric algebra of a module are introduced and their arithmetical and homological properties studied. Emphasis is placed on converting syzygetic properties of the modules into ideal theoretic properties of the algebras, e.g. Cohen-Macaulayness, factoriality. The main tools are certain Fitting ideals of the module and an extension to modules of a complex of not necessarily free modules that we have used in studying blowing-up rings.

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