On the length of generalized fractions

A Study of the Length Function of Generalized Fractions of Modules

“…By considering all explicit examples, it can be expected that J x,M (n) coincides with finitely many polynomials in n (cf. [10], [20]). As we will see this is not always the case.…”

Idealizations of Pseudo Buchsbaum Modules Over a Pseudo Buchsbaum Ring

“…Unfortunately, Cuong-Morales-Nhan [6] gave a counterexample to show that, in general J M (a(n)) is not a polynomial for n ≫ 0. However, we have the following important result, cf.…”

“…In [13], K. Yamagishi clarified the condition for the idealization of Buchsbaum rings and modules to be Buchsbaum. Recently, Cuong-Morales-Nhan [6] used successively the notion of idealization in order to answer an open question by on the polynomial property of the length of fractions.…”

The finiteness of certain sets of attached prime ideals and the length of generalized fractions

“…This least degree is denoted by pf(M ). When pf(M ) ¿ 0, it has been shown in [4,Theorem 1.2], for several special cases that q x;M (n) is not a polynomial for n large enough, for some system of parameters x of M . By using strict f-sequences, we can extend this result to the general case.…”