RELATIVE ATTACHED PRIMES AND COREGULAR SEQUENCES

Abstract

We extend the existing concepts of secondary representation of a module, coregular sequence and attached prime ideals to the more general setting of any hereditary torsion theory. We prove that any $\tau$-artinian module is $\tau$-representable and that such a representation has some sort of unicity in terms of the set of $\tau$-attached prime ideals associated to it. Then we use $\tau$-coregular sequences to find a nice way to compute the relative width of a module. Finally we give some connections with the relative local homology.