Relative attached primes and coregular sequences (Q390084)

Let \(R\) be a commutative unital ring and \(\tau\) a hereditary torsion theory on the category \(R\)-mod of all unital \(R\)-modules. The aim of this paper is introduce and study the relative versions with respect to \(\tau\) of the concepts of secondary representation of a module, coregular sequence, and attached prime ideal of a module. Among others, the authors prove that any \(\tau\)-Artinian module has a minimal \(\tau\)-secondary representation.