Type-sequences of modules (Q5939851)

Let \(R\) be a Noetherian complete local domain of dimension \(1\). In the present paper, the authors define the type sequence \([r_1, \dots, r_n]\) of a fractional ideal \(M\) of \(R\), where \(r_1\) is the Cohen-Macaulay type of \(M\), and they investigate its behavior. An ideal is said to have minimal type sequence if its type sequence is \([r, 1, \dots, 1]\). For example, the canonical ideal has minimal type sequence. The ring \(R\) has minimal type sequence if and only if \(R\) is almost Gorenstein.NEWLINENEWLINENEWLINEThis paper gives some characterization of minimal type sequence ideals and shows that \(R\) is almost Gorenstein if and only if all the fractional ideals have minimal type sequence.