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To each finitely presented module over a commutative ring one can associate an -ideal , which is called the (zeroth) Fitting ideal of over . This is of interest because it is always contained in the -annihilator of , but is often much easier to compute. This notion has recently been generalised to that of so-called ‘Fitting invariants’ over certain noncommutative rings; the present author considered the case in which is an -order in a finite dimensional separable algebra, where is an integrally closed commutative noetherian complete local domain. This article is a survey of known results and open problems in this context. In particular, we investigate the behaviour of Fitting invariants under direct sums. In the appendix, we present a new approach to Fitting invariants via Morita equivalence.
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Published: 1 January 2020
First available in Project Euclid: 12 January 2021