On infinite direct products of copies of a Dedekind domain

[摘要] Let kappa be an infinite cardinal number and let R-kappa be the direct product of kappa copies of a Dedekind domain R which is not a field or a complete discrete valuation ring. If R-kappa equals A + B as an R-module, then A congruent to R-kappa or B congruent to R-kappa. If kappa < mu, the lease measurable cardinal number, or \R\ < kappa = mu, then any direct summand of R-kappa is isomorphic to a direct product of ideals in R. An infinite direct product of nonzero ideals in R is isomorphic to R-alpha for some infinite alpha. (C) 1997 Academic Press.

[发布日期] 1997-06-15