This paper gives the additivity and reduction formulas for mixed multiplicities of multi-graded
modules M and mixed multiplicities of arbitrary ideals, and establishes the recursion …

Let $(A,\frak m) $ be a noetherian local ring with maximal ideal $\frak {m} $ and infinite
residue field $ k= A/\frak {m}. $ Let $ J $ be an $\frak m $-primary ideal, $ I_1,\ldots, I_s …

The paper proves that the superficial sequences in [13, 15, 16, 25] are the weak-(FC)-
sequences in [18]. This follows that [18, Theorem 3.4] of Viet in 2000 covers the results of …

The original mixed multiplicity theory considered the class of mixed multiplicities concerning
the terms of highest total degree in the Hilbert polynomial. This paper defines a broader …

Mixed multiplicities and the multiplicity of Rees modules of reductions Page 1 Journal of Algebra
and Its Applications Vol. 18, No. 9 (2019) 1950176 (13 pages) c© World Scientific Publishing …

Let $ S $ be an $\mathbf {N}^ d $-graded algebra over a noetherian ring and a finitely
generated $\mathbf {N}^ d $-graded $ S $-module $ M $. This paper will study the …

This paper defines the Euler–Poincaré characteristic of joint reductions of ideals which
concerns the maximal terms in the Hilbert polynomial; characterizes the positivity of mixed …

This paper gives the recursion formula for mixed multiplicities of maximal degrees with
respect to joint reductions of ideals, which is one of important results in the mixed multiplicity …

In the direction towards the question when mixed multiplicities are equal to the Hilbert–
Samuel multiplicity of joint reductions, this paper not only generalizes Viet et al.(Proc Am …

Let $(R,\mathfrak m) $ be a Noetherian local ring. In this work we extend the notion of mixed
multiplicities of modules, given in\cite {Kleiman-Thorup2} and\cite {Kirby-Rees1}(see …