2017/12/20 by Andreas Nickel, Nickel, Andreas
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1712.07368
openalex publication_date 2017/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To each finitely presented module M over a commutative ring R one can associate an R-ideal FittR(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 AnnR(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 \mathfrako-order Λ in a finite dimensional separable algebra, where \mathfrako 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.