Trace Ideals and Centers of Endomorphism Rings of Modules over Commutative Rings

By H. Lindo. 2016

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Let $R$ be a commutative Noetherian ring and $M$ a finitely generated $R$-module. Under various hypotheses, it is proved that the center of $\mbox{End}_R(M)$ coincides with the endomorphism ring of the trace ideal of $M$. These results are exploited to establish results for balanced and rigid modules, and to settle certain cases of a conjecture of Huneke and Wiegand.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/445890714dca5fac59ef09d831c94d015db1ff03