Showing papers in "Journal of Pure and Applied Algebra in 1998"

TL;DR: In this article, the authors considered a simplicial complex Δ ∗ which is in a sense a canonical Alexander dual to Δ and showed that it is possible to compute the Betti numbers dimk ToriA (k[Δ],k) in some cases where Δ∗ is wellbehaved (shellable, Cohen-Macaulay or Buchsbaum).

TL;DR: In this article, the authors present an algorithm to determine if a real polynomial is a sum of squares (of polynomials) and to find an explicit representation if it is.

TL;DR: A new method for solving symbolically zero-dimensional polynomial equation systems in the affine and toric case using Newton iteration in order to simplify straight-line programs occurring in elimination procedures and improving the well-know worst-case complexity bounds for zero- dimensional equation solving in symbolic and numeric computing.

TL;DR: In this paper, it was shown that two flat differential graded algebras whose derived categories are equivalent by a derived functor have isomorphic cyclic homology, and that under suitable flatness hypotheses, an exact sequence of derived categories of DG algesbras yields a long exact sequence in cyclical homology.

TL;DR: In this paper, sufficient conditions for the supersolubility of finite groups are given under the assumption that the maximal subgroups of Sylow subgroups are well-situated in the group.

TL;DR: In this paper, the regular and exact completions of categories with weak limits are proved and to be determined by an appropriate universal property, and several examples are discussed, and in particular the class of examples given by categories monadic over a power of Set.

TL;DR: In this paper, the concept of gauge transformations of quasi-Hopf algebras is used to study algebraic structures based on actions of a bialgebra and relate this to the theory of universal deformation formulas.

TL;DR: In this article, it was shown that the dimension of any irreducible module for a finite-dimensional Hopf algebra over an algebraically closed field is not the same as that of any cross product of the algebra with a group algebra or its dual, provided the characteristic of the field does not divide the order of the group.

TL;DR: In this article, a complete classification up to isomorphisms of complex filiform Lie algebras of dimension m with m ≤ 11 is given. But this classification is restricted to isomorphic isomorphism.

TL;DR: Hopf (bi-) modules and crossed modules over a bialgebra B in a braided monoidal category C are considered in this paper, and the equivalence of both categories is proved provided B is a Hopf algebra (with invertible antipode).

TL;DR: In this article, a finite, free resolution of the integers over the group ring of a group admits the structure of an iterated semidirect product of finitely generated free groups.

TL;DR: In this paper, the authors consider the theory of operads and their algebras in enriched category theory and introduce the notion of simplicial A∞-graph and show that some important constructions of homotopy coherent category theory lead by a natural way to the use of such objects as the appropriate homogopy coherent counterparts of the categories.

TL;DR: In this article, two complementary questions for semidirect products and pseudovarieties of semigroups are addressed: to determine when a pseudo-identity is valid in a semigroup and to find a basis of pseudoidentities.

TL;DR: An algorithm for the computation of real radicals of polynomial ideals and results concerning the computational requirements and the complexity as well as some theoretical consequences are presented.

TL;DR: In this paper, the essentially final positive answer to the isomorphism problem for monoid rings of submonoids of Zr is obtained, which means that the underlying monoid is shown to be determined by the corresponding monoid ring.

TL;DR: In this paper, basic results for an algebraic treatment of commutative and non-commutative Poisson algebras are described, and a ring-theoretic approach to Symplectic Algebraic Poisson Algebra is presented.

TL;DR: In this paper, the authors give an algorithmic method to compute a minimal system of generators for I, in the general case of a subsemigroup S of a finitely generated abelian group, such that S∩(S) = 0.

TL;DR: In this paper, minimal free resolutions for homogeneous ideals corresponding to certain 0-dimensional subschemes of P2 defined by sheaves of complete ideals are determined implicitly over an algebraically closed field of arbitrary characteristic.

TL;DR: In this paper, the notion of a categorically compact topological group was studied, and the following results were proved: (1) any product of C-compact topological groups is compact; (2) separable C -compact groups are totally minimal; and (3) C −compact soluble topological clusters are compact.

TL;DR: In this article, the authors studied the polynomial representation theory of general linear groups over an infinite field with the property that their representation theory is graded in a natural way, and characterized the associated Schur algebras as centralizers for the Brauer algesbras, in characteristic zero.

TL;DR: In this article, a general result about commuting actions on certain objects in braided rigid monoidal categories is derived, which enables us to define an action of the Brauer algebra on the tensor space V⊗k which commutes with the action of orthosymplectic Lie superalgebra spo(V) and the orthosymmplectic lie color algebra spo (V, β).

TL;DR: In this article, it was shown that any generalized Kac-Moody Lie algebra g that has no mutually orthogonal imaginary simple roots can be written as g = u + ⊕ (g J + h )⊕ u −, where g J is defined from a symmetrizable Cartan matrix, and u + and u − are subalgebras isomorphic to free Lie algebra over certain g J-modules.

TL;DR: In this article, the dimension of the open subset of the Hilbert scheme, Hilbp(t)Pn, parametrizing AG closed subschemes X ⊂ Pn of codimension 3 was computed.

TL;DR: In this article, a presentation by generators and relations for K 1 of an arbitrary exact category is given, where the generator and relations are given by a generator and a relation for each exact category.

TL;DR: In this article, it was shown that every topos with enough points is equivalent to the classifying topos of a topological groupoid, and that the topology of a groupoid can be represented as a topology.

TL;DR: In this article, it was shown that FC-type Artin groups are asynchronously automatic and that the set of positive words in a standard presentation of an Artin group of FC type is isomorphic to the monoid given by the same presentation.

TL;DR: In this article, the authors compute the Leibniz homology of the dialgebra of matrices with entries in a given dialgebra D with respect to the tensor module over HHS (D), which is a variation of the natural dialgebra homology HHY (D ).

TL;DR: In this article, it was shown that for any finite dimensional, split basic algebra λ = KΓ I, there is a finite list of affine algebraic varieties, the points of which correspond in a natural fashion to the isomorphism types of uniserial left Λ-modules, and the geometry of which faithfully reflects the constraints met in constructing such modules.

TL;DR: In this article, the authors give a definition of groups of homology and cohomology with coefficients, for an algebra over a quadratic operad in characteristic zero, and study the relation between their theory and the theory of Barr-Beck's homology.

TL;DR: In this article, various constructions on a given bialgebra B, producing bialgebras with extra structure are described in terms of the monoidal category of representations of B.