2015/08/18 by Andreas Reinhart, Reinhart, Andreas
Mathematics · #13A15 #13F05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A15 #msc:13F05
paper · pdf · doi:10.48550/arxiv.1508.04260
arxiv created 2015/08/18 · arxiv updated 2015/08/19
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 criterions 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 papers. We sketch the boundaries of our criterions by providing a few counterexamples.