Some remarks on the ring

Eljeri, Mosbah; Benhissi, Ali

doi:10.1007/s12215-011-0033-7

Search citation statements

Order By: Relevance

Paper Sections

Select...

Theorem 7 D Is a Krull Domain If And Only If D X Is A Krull1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2012

2017

Publication Types

Select...

Article2

Book1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [4], Eljeri and Benhissi first introduced the ring D X ℵ 0 , where they denoted D X ℵ 0 by D X 4 , and they then in [3] studied some ringtheoretic properties of D X 4 . Among other things, they proved that (1) if for each finite n, D X 1 X n is a UFD then D X 4 is a UFD and (2) if D is a Krull domain then D X 4 is a Krull domain.…”

Section: Theorem 7 D Is a Krull Domain If And Only If D X Is A Krullmentioning

confidence: 99%

Rings of Formal Power Series in an Infinite Set of Indeterminates

Chang¹

2014

Communications in Algebra

View full text Add to dashboard Cite

Let be an infinite cardinal number, be an index set of cardinality > , and X ∈ be a set of indeterminates over an integral domain D. It is well known that there are three ways of defining the ring of formal power series in X ∈ over D, say, D X i for i = 1 2 3. In this paper, we let D X = ∪ D X ∈ 3 ⊆ and ≤ , and we then show that D X is an integral domain such that D X 2 D X D X 3 . We also prove that (1) D is a Krull domain if and only if D X is a Krull domain and (2) D Xis a unique factorization domain (UFD) (resp., -domain) if and only if D X 1 X n is a UFD (resp., -domain) for every integer n ≥ 1.

show abstract

Section: Theorem 7 D Is a Krull Domain If And Only If D X Is A Krullmentioning

confidence: 99%