Showing papers in "Journal of Pure and Applied Algebra in 1997"

TL;DR: In this paper, a linearization of the distributivity of product over sum is proposed to model Gentzen's cut rule and can be strengthened in two natural ways to generate full distributivity and ∗autonomous categories.

TL;DR: In this article, it was shown that if M is a finitely generated module over a commutative Noetherian local ring R and I is a dimension one ideal of R (i.e., dim R I = 1 ), then the local cohomology modules H I i (M ) are I -cofinite; that is, Ext R j (R I, H I I i ) is finitely generate for all i, j.

TL;DR: An intrinsic lower bound for the logarithmic height of diophantine approximations to a given solution of a zero-dimensional polynomial equation system is obtained and represents a multivariate version of Liouville's classical theorem on approximation of algebraic numbers by rationals.

TL;DR: In this article, the approximate GCD of two univariate polynomials given with limited accuracy is studied, where the singular values of the Sylvester matrix singular values are used to establish a gap theorem on certain singular values that certifies the maximum degree of the GCD.

TL;DR: In this article, it was shown that the stable homotopy theory of simplicial B-algebras is equivalent to the stable theory of augmented commutative simplicial ring B. In terms of this equivalence, we can identify Andre-Quillen homology as a stabilization process.

TL;DR: In this paper, the authors use the correspondence between ideals of R and vector spaces of K, stable by derivation and closed for the (∂)-adic topology, in order to construct the local inverse system of an isolated point.

TL;DR: In this article, a topology on the spectrum of a locally coherent Grothendieck category is introduced, where closed subsets are related to certain localizing subcategories which are characterized in terms of Serre sub-categories of the full subcategory of finitely presented objects.

TL;DR: In this paper, the suspension-loop construction is used to define a process in a symmetric monoidal category, and the algebra of such processes is defined in terms of symmetric Monoidal bicategories.

TL;DR: In this article, the authors studied the minimal free resolution of a ring T = S I where S is a positive affine semi-group ring over a field K, and I is an ideal in S generated by monomials.

TL;DR: Algorithms for computing the b-function (Bernstein-Sato polynomial) of f, the D-module (the system of linear partial dierential equations) for f s is presented.

TL;DR: In this paper, an explicit formula of an important normalization factor, which is the value of the trivial knot, in the universal enveloping algebra U(g) of any Lie algebra is given.

TL;DR: In this article, the concept of higher-order differential operators on a general noncommutative, nonassociative superalgebra A, and a vertex operator super algebra (VOSA) has been defined, namely modes of vertex operators.

TL;DR: In this article, the authors consider the problem of determining the dimension of the space of bivariate splines Ckr(Δ), for all k. This problem is closely related to the question of whether Cr(\gD) is a free R-module.

TL;DR: In this paper, the authors studied the decomposition of the elements of a group given by a presentation as quotients of positive elements (the elements of G that can be expressed without using the inverses of the generators) in the special case when the presentation satisfies some syntactical condition.

TL;DR: In this article, the authors discuss various moduli problems involving the classification of finite subgroups or related structures on formal groups of finite height n. They show that many moduli schemes are smooth or at least Cohen-Macaulay.

TL;DR: In this article, it was shown that the 2-category of tensored W-categories and all W-functors between them is equivalent to the 2 -category of closed W-representations and maps of such, which in turn is isomorphic to a full sub-2-category Lax(W, Cat).

TL;DR: In this article, it was shown that the topological Hochschild homology spectrum of an E ∞ spectrum R is the S 1 -indexed sum of copies R in the category of ring spectra.

TL;DR: In this article, a natural wellordering on the free monoid on infinitely many generators by representing words as trees was developed, which corresponds to the restriction of Dehornoy's ordering to positive braids.

TL;DR: If V(L) is the vector space of solutions of L(y) = 0, it is shown how given some integer m, one can compute the elements of the symmetric power Symm(V(L)) that are left fixed by the Galois group.

TL;DR: In this paper, the stabilization T → StabT is characterized by a universal property, which permits a perspicuous proof of the existence of coherent symmetric smash product in the standard stable homotopy theory.

TL;DR: In this paper, a new algorithm for computing standard and multi-graded Hilbert-Poincare series of a monomial ideal is described, along with implementation details and timing data.

TL;DR: A method is presented that reduces the problem of computing the radical of a matrix algebra over an arbitrary field to solving systems of semilinear equations and a simple test for isomorphism of semisimple modules is presented.

TL;DR: In this article, the total sum of Grothendieck residues of a Laurent polynomial relative to a family of polynomials in n variables with a set of common zeroes in the torus T = (C! ) n.

TL;DR: In this article, it was shown that the embeddability of a finite 4-nilpotent semigroup into a 0-simple finite semigroup with maximal groups from a pseudovariety V is decidable if and only if the universal theory of the class V was decidable.

TL;DR: In this paper, it was shown that R is right weakly π-regular and WCI satisfies WCI, where WCI is the condition that every prime ideal of R is maximal.

TL;DR: In this paper, a new effective nullstellensatz with bounds for the degrees which depend not only on the number of variables and on the degrees of the input polynomials but also on an additional parameter called the geometric degree of the system of equations was presented.

TL;DR: In this article, it was shown that the logarithmic derivative of such a form F, evaluated in the solutions of L ( y ) = 0, is the first coefficient of a polynomial P ( u ) whose zeros are log-arithm derivatives of the solution of L( y) = 0.

TL;DR: In this paper, the authors show that the set of nonsmooth points of the morphism Spec B → Spec A has codimension greater than one in Spec B. They also give a jacobian formula for certain locally nilpotent derivations of k[X1, …, Xn].

TL;DR: In this article, the authors show how recent progress in non-commutative combinatorial algebra gives a new input to Jacobian-related problems in a commutative situation.

TL;DR: In this paper, the concept of sketch is generalized and a semantics and a deductive calculus of sketch-entailments are developed, and a General Completeness Theorem (GCT) is given.