Showing papers in "Journal of Algebra in 1988"

TL;DR: In this article, the authors present the idea of coloring of a commutative ring and show that the existence of an infinite clique implies that the clique R = co implies that there exists an infinitely many cliques.

TL;DR: In this article, a classe d'algebres de Lie qui ont une forme bilineaire contravariante qui est presque definie positive is discussed.

TL;DR: In this article, it was shown that the fourth power of the antipode is the identity in a finite-dimensional Hopf algebra over a field of characteristic 0, which is a conjecture mentioned by Kaplansky [I].

TL;DR: In this paper, Carles et al. showed that the homomorphic image of a nilpotent Lie algebra is in the closure of the orbit of that Lie algebra (taking the direct product with an abelian Lie algebra to make the dimension right).

TL;DR: The basic facts on skew polynomials in the (S, D)-setting are developed, the evaluation of such polynomial ring K is defined, and the all-important “Product Theorem” is proved.

TL;DR: Soit L une algebre de Lie simple restreinte de dimension finie sur un corps algebriquement clos F de caracteristique p>7.

TL;DR: In this paper, a factorization of the canonical map R → S as a composition of a complete intersection R → C with a Golod map C → S is presented, which is accomplished by invoking a theorem of Avramov and Backelin once one has existence of a DGΓ-algebra structure on a minimal R -free resolution of S together with detailed knowledge of the structure of the induced homology algebra Tor R (S, k ) = H ( K S ).

TL;DR: In this article, the authors considered the case where S is a Gorenstein log de 1 Pezzo surface and showed that it is a Cartier divisor if and only if S has rational double points.

TL;DR: In this article, general results concerning derivations of finitely generated Lie algebras are established, which are employed in order to determine the derivations and central extensions of Kac-Moody Lie algesbras.

TL;DR: In this article, the authors define the category of all right (resp. left) A-modules for an artin algebra A and the ordinary duality functor is denoted by D: mod-A 2 A-mod, i.e., D = Hom,(?, f) with the minimal injective cogenerator I over k.

TL;DR: In this article, the structure of a 2-dimensional normal local domain (S, n) is examined from an algebraic point of view, primarily from a geometric perspective, and it is shown that S must have minimal multiplicity.

TL;DR: In this article, the arithmetical rank of monomial ideals has been studied by several authors and it has been shown that every algebraic set of pure codimension t can be set-theoretically cut out by n [n/t] + 1 hypersurfaces.

TL;DR: In this article, the relative position of any two components of PU (in general an element of the Weyl group, in the present case a subset of S) is given, in terms of the corresponding tableaux, by the RobinsonSchensted correspondence.

TL;DR: In this article, the authors give a proof of Lemma 4 (see Section 1) for the sake of convenience and make some remarks on the local cohomology modules of Rees rings.

TL;DR: In this paper, it was shown that every matrix in SLnR is the product of at most c commutators, where R ranges over euclidean commutative rings and n ⩾ 3.

TL;DR: In this article, the authors classify the nilpotent orbits of G0 in g0 (for the adjoint action) by using Kostant's conjecture, which was recently proved by J. Sekiguchi and the author.

TL;DR: In this paper, the authors obtained new properties connected with the number of conjugacy classes of elements of a finite group, through the analysis of the numberr G(gN), where n is a normal subgroup of a group and g any element of the group.

TL;DR: In this article, the integrable modules with finite-dimensional weight spaces for twisted aftine Lie algebras have been studied, where the centre acts non-trivially.

TL;DR: In this article, the congruence structure of a group is used to characterize its linearity, and a characterization of finitely generated linear groups over a field of characteristic zero is given.

TL;DR: In this paper, the authors considered the distribution of coefficients of a Coxeter matrices of W, S in a group of parties commutatives of IX(S) and found that the distribution is a function of the number of coeffkients.