2021•Contemporary mathematics - American Mathematical SocietyOpen access

Dimension of finite free complexes over commutative Noetherian rings

Lars Winther Christensen, Srikanth B. Iyengar

Abstract

Foxby defined the (Krull) dimension of a complex of modules over a commutative Noetherian ring in terms of the dimension of its homology modules. In this note it is proved that the dimension of a bounded complex of free modules of finite rank can be computed directly from the matrices representing the differentials of the complex.

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Key concepts: Krull dimension, Global dimension, Noetherian, Mathematics, Local ring, Commutative property, Pure mathematics, Dimension theory (algebra)