Let R be a Cohen-Macaulay local ring with maximal ideal m. In this paper we present a procedure for computing the coefficient ideals, in particular the Ratllif-Rush closure, of a m−primary ideal I ⊂ R.

Generic linkage is used to compute a prime ideal such that the radical of the initial ideal of the prime ideal is equal to the radical of a given codimension two monomial ideal that has a Cohen-Macaulay quotient ring.

This paper shows that if [Formula: see text] is a homomorphic image of Cohen–Macaulay local ring, then text]-module sequentially generalized and only the difference between Hilbert coefficients arithmetic degrees for all distinguished parameter ideals are bounded.

Let KV ] G be the invariant ring of a nite linear group G GL(V), and let GU be the pointwise stabilizer of a subspace U V. We prove that the following numbers associated to the invariant ring decrease if one passes from KV ] G to KV ] G U : the minimal number of homogeneous generators, the maximal degree of the generators, the number of syzygies and other Betti numbers, the complete intersectio...

Let K[V ] be the invariant ring of a finite linear group G ≤ GL(V ), and let GU be the pointwise stabilizer of a subspace U ≤ V . We prove that the following numbers associated to the invariant ring do not increase if one passes from K[V ] to K[V ]U : the minimal number of homogeneous generators, the maximal degree of the generators, the number of syzygies and other Betti numbers, the complete ...

Pseudomonomials and ideals generated by pseudomonomials (pseudomonomial ideals) are a central object of study in the theory of neural rings and neural codes. In the setting of a polynomial ring, we define the polarization operation ρ sending pseudomonomials to squarefree monomials and a further polarization operation P sending pseudomonomial ideals to squarefree monomial ideals. We show for a p...

To reduce to resolving Cohen–Macaulay singularities, Faltings initiated the program of “Macaulayfying” a given Noetherian scheme X. For wide class X, Kawasaki built sought-for modifications, with crucial drawback that his blowups did not preserve locus CM(X)?X, where X is already Cohen–Macaulay. We extend Kawasaki’s methods show every quasi-excellent, has X˜ proper map X˜?X an isomorphism over ...

We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has minimal reduction. When this is case, we study Cohen–Macaulay and Gorenstein properties associated graded provide several bounds for reduction number with respect to

To every directed graph G one can associate a complex (G) consisting of directed subforests. This construction, suggested to us by R. Stanley, is especially important in the case of a complete double directed graph Gn, where it leads to studying some interesting representations of the symmetric group and corresponds (via Stanley-Reisner correspondence) to an interesting quotient ring. Our main ...

New upper bounds on the first and second Hilbert coefficients of a Cohen-Macaulay module over local ring are given. Characterizations provided for some to be attained. The characterizations given in terms series as well Castelnuovo-Mumford regularity associated graded module.