Turkish Journal of Mathematics
DOI
10.3906/mat-1307-24
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.
Keywords
Krull ring, ring of Krull type, valuation Marot ring
First Page
614
Last Page
624
Recommended Citation
SAYLAM, BAŞAK AY
(2014)
"On density theorems for rings of Krull type with zero divisors,"
Turkish Journal of Mathematics: Vol. 38:
No.
4, Article 2.
https://doi.org/10.3906/mat-1307-24
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss4/2
