On density theorems for rings of Krull type with zero divisors

Authors : Başak Ay Saylam

Pages : 614-624

Doi:10.3906/mat-1307-24

View : 13 | Download : 9

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :Let R be a commutative ring and I(R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A \leqslant B if and only if B \subseteq A. If R is a Marot ring of Krull type, then R(Pi), where {Pi}i \in I are a collection of prime regular ideals of R, is a valuation ring and R = \bigcap R(Pi). We denote by Gi the value group of the valuation associated with R(Pi). We prove that there is an order homomorphism from I(R) into the cardinal direct sum \coprodi \in I Gi and we investigate the conditions that make this monomorphism onto for R.
Keywords : Krull ring, ring of Krull type, valuation Marot ring