Soundable Subsets of a Spectrum and Depth
Gabriel Pıcavet · 2023
This chapter represents a summary of the author’s talk given at the Fes algebra meeting. The results will be published in a forthcoming paper together with their proofs and various other developments. The chapter shows that the assassin is a soundable subset of the spectrum of A. The main purpose is the study of such soundable subsets, as well as closely related ideas. The chapter considers M be an A-module, then the A[t]-moduleM[t] is soundable. A finite Goldie dimensional A-module is soundable. An A-module is soundable if and only if its injective envelope is soundable. An A-module with an irreducible zero submodule is soundable and primal. Clearly, a Bezout domain is absolutely soundable. One can also show that a ring of continuous real functions is absolutely soundable.