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• W2777861766 abstract "To each finitely presented module $M$ over a commutative ring $R$ one can associate an $R$-ideal $mathrm{Fitt}_{R}(M)$, which is called the (zeroth) Fitting ideal of $M$ over $R$. This is of interest because it is always contained in the $R$-annihilator $mathrm{Ann}_{R}(M)$ of $M$, 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 $R$ is an $mathfrak{o}$-order $Lambda$ in a finite dimensional separable algebra, where $mathfrak{o}$ 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." @default.
• W2777861766 created "2018-01-05" @default.
• W2777861766 creator A5084350670 @default.
• W2777861766 date "2017-12-20" @default.
• W2777861766 modified "2023-09-27" @default.
• W2777861766 title "Notes on noncommutative Fitting invariants" @default.
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• W2777861766 hasPublicationYear "2017" @default.
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