A Note on Conductor Ideals. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Reinhart, Andreas
• Is Part Of: Communications in algebra. Volume 44:Issue 10(2016)
• Page Start: 4243
• Page End: 4251
• Publication Date: 2016-10-02
• Subjects: Conductor -- Dedekind domain -- Ring extension; 13A15 -- 13F05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1087539
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Let S be a commutative ring with identity and R a unitary subring of S . An ideal I of S is called an R -conductor ideal of S if I = { x ∈ S | xS ⊆ V } for some intermediate ring V of R and S . In this note, we present necessary and sufficient criteria for being an R -conductor ideal of S . We generalize several well known facts about them and present a simple approach to rediscover the results of both old and recent articles. We sketch the boundaries of our criteria by providing a few counterexamples.