Quasi-unmixedness and integral closure of Rees rings

Peter G. Sawtelle
1976 Proceedings of the American Mathematical Society  
For certain Rees rings 91 of a local domain R, the quasiunmixedness of R is characterized in terms of a certain transform of 9t being contained in the integral closure of 9L 1. Introduction. In this paper, a ring shall be a commutative ring with identity. The terminology is basically that of [2] and [12]. Relations between quasi-unmixedness and integral extensions are well known (e.g., [1], [5] and [7]). Also, the study of properties of a ring R via transition to a Rees ring 91 = 9l(R,A) of R
more » ... 91 = 9l(R,A) of R (conditions on the ideal A depending on the particular discussion) has often been useful. In particular, characterizations of the quasi-unmixedness of R are given in [10] in terms of localizations of 91 containing R as a quasi-subspace. The 6!^algebra 9" = <í}(u9¿) (Definition 1) is used in [8] to characterize unmixed local domains. Here, equivalences to the quasi-unmixedness of R are given in terms of 5" being contained in the integral closure of 91 (Theorem 2).
doi:10.1090/s0002-9939-1976-0399073-0 fatcat:hkvt7enjw5cu5h3a5l6tuta7xa