RELATIVE ATTACHED PRIMES AND COREGULAR SEQUENCES

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.