Abelian lattice-ordered groups and a characterization of the maximal spectrum of a Prüfer domain

Autores: Wolfgang Rump
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 218, Nº 12, 2014, págs. 2204-2217
Idioma: inglés
DOI: 10.1016/j.jpaa.2014.03.011
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Resumen
- The concept of z -projectable abelian lattice-ordered group is introduced, and it is shown that every such group G can be identified with the group of global sections of a sheaf GG with totally ordered stalks on the co-Zariski space Min G of minimal prime ideals. Semi-projectable abelian l -groups are z -projectable, but not vice versa. The sheaves GG as well as the spaces Min G arising from abelian l-groups G are characterized completely. Using Hochster duality and the Jaffard�Ohm correspondence, the results are applied to determine the maximal spectrum of a Prüfer domain and of a Bézout domain.