Turkish Journal of Mathematics
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_{(P_i)}, where {P_i}_{i \in I} are a collection of prime regular ideals of R, is a valuation ring and R = \bigcap R_{(P_i)}. We denote by G_i the value group of the valuation associated with R_{(P_i)}. We prove that there is an order homomorphism from I(R) into the cardinal direct sum \coprod_{i \in I} G_i and we investigate the conditions that make this monomorphism onto for R.
DOI
10.3906/mat-1307-24
Keywords
Krull ring, ring of Krull type, valuation Marot ring
First Page
614
Last Page
624
Recommended Citation
SAYLAM, B. A (2014). On density theorems for rings of Krull type with zero divisors. Turkish Journal of Mathematics 38 (4): 614-624. https://doi.org/10.3906/mat-1307-24
