Journal article
Half condensed domains
Houston Journal of Mathematics, Vol.30(4), pp.929-936
2004
Abstract
An integral domain D is condensed (resp., strongly condensed) if for each pair of ideals I, J of D, I J = {ij; i ∈ I, j ∈ J} (resp., I J = i j for some i ∈ I or I J = I j for some j ∈ J), In this paper we introduce and study the two related notions of a half condensed domain and a strongly half condensed domain. An integral domain D is half condensed if whenever 0 ≠ z ∈ I J with I, J ideals of D, there exist I′, J′ (invertible) ideals of D such that I′ ⊆ I, J′ ⊆ J and zD = I′ J′. And D is strongly half condensed if whenever I, J are nonzero ideals of D, I J = I1 J for some invertible ideal I 1 ⊆ I or I J = I J1 for some invertible ideal J 1 ⊆ J.
Details
- Title: Subtitle
- Half condensed domains
- Creators
- D.D. AndersonTiberiu Dumitrescu
- Resource Type
- Journal article
- Publication Details
- Houston Journal of Mathematics, Vol.30(4), pp.929-936
- Publisher
- University of Houston
- ISSN
- 0362-1588
- Language
- English
- Date published
- 2004
- Academic Unit
- Mathematics
- Record Identifier
- 9984230420102771
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