ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 13C99 Lu, Sylvia C., University of Colorado, USA The Zariski topology on the prime spectrum of a module. Let M be a module over a commutative ring R with identity, X = Spec(M) the collection of all prime submodules of M, and ψ : Spec(M) → Spec(R/Ann(M)) the natural map defined by ψ(P) = (P : M) + Ann(M) for every P ∈ X. In this talk, a topology on the prime spectrum X of M, named the Zariski topology, will be introduced and compared with the Zariski toplogy on Spec(R) from the point of view of spectral topological spaces. Results of the investigation indicate that the injectivity and the surjectivity of the natural map ψ play, respectively, important roles for X being a spectral space or satisfying partial condition(s) to be spectral. References: C. P. Lu, Spectra of modules, Comm. Algebra, 23(10) (1995), 3741-4752.