Journal article
Two star-operations and their induced lattices
Communications in Algebra, Vol.28(5), pp.2461-2475
01/01/2000
DOI: 10.1080/00927870008826970
Abstract
Let D be an integral domain with quotient field K, let (F(D) (f(D)) be the set of nonzero (finitely generated) fractional ideals of D, and let ★ be a star-operation on F(D).For A ∈ F(D) and there exists J∈f(D) such that J ★ =D, and xJ ⊆ A}.Then A ★w = {x ∈ K | exists J ∈ f(D) such that J ★ = D, and xJ ⊆ A}. Then and ★ w are star-operations on F(D) that satisfy . Moreover, is the greatest (finite character) star-operation Δ ≤ ★ with (A ∩B) Δ =A Δ ∩ B Δ .We also show that ★ w -Max(D)= ★ s -Max(D) and A ★w =∩{A P | P ∈★ s -Max(D)}.Let L ★w (D) = {A | A is an integral ★ w -ideal}∪{0}. Then L ★w (D) forms an r-lattice. If D satisfies ACC on integral ★ w -ideals,L *w (D) is a Noether lattice and hence primary decomposition, the Krull intersection theorem, and the principal ideal theorem hold for * w -ideals of D. For the case of ★=υ,★ w is the w-operation introduced by Wang Fanggui and R.L. McCasland.
Details
- Title: Subtitle
- Two star-operations and their induced lattices
- Creators
- D.D Anderson - Department of Mathematics , The University of IowaS.J Cook - Department of Mathematics , The University of Iowa
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.28(5), pp.2461-2475
- Publisher
- Gordon and Breach Science Publishers Ltd
- DOI
- 10.1080/00927870008826970
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 01/01/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9983985878802771
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