On density theorems for rings of Krull type with zero divisors | Zendy

Başak Ay Saylam | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On density theorems for rings of Krull type with zero divisors

Author(s) -

Başak Ay Saylam

Publication year - 2014

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1307-24

Subject(s) - mathematics , multiplicative function , monomorphism , invertible matrix , commutative ring , homomorphism , valuation ring , category of rings , krull dimension , noncommutative ring , combinatorics , pure mathematics , principal ideal ring , ring (chemistry) , discrete mathematics , commutative property , algebra over a field , noetherian , injective function , mathematical analysis , field (mathematics) , chemistry , organic chemistry

Let R be a commutative ring and I(R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A ≥ B if and only if B ⊆ A. If R is a Marot ring of Krull type, then R(Pi), where {Pi}i∈I are a collection of prime regular ideals of R, is a valuation ring and R = ∩ 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 ∐i∈I Gi and we investigate the conditions that make this monomorphism onto for R

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research