Showing papers in "Journal of Algebra in 2000"

TL;DR: In this paper, the relationships between Armendariz rings and reduced rings were investigated, and several examples and counterexamples are included for answers to questions that occur naturally in the process of this paper.

TL;DR: In this article, it was shown that the set of all possible n's is exactly the collection of N -combinations of the prime divisors of a given natural number m, where n denotes the subset of all non-negative integers in m. The proof is long and involves a subtle analysis of minimal vanishing sums of mth roots of unity.

TL;DR: In this article, it was shown that the i-linear strand of the minimal free resolution of a Stanley-Reisner ideal IΔ⊂ S has the same information as the module structure of ExtiS(k[Δ∨,], εS), where Δ∨ is the Alexander dual of Δ.

TL;DR: In this article, it was shown that, allowing equality, the bound 1/10 can be replaced by 13/42; and, excluding an explicitly listed set of simple groups, 2/3 holds.

TL;DR: In this paper, the authors studied the relation between a finite-dimensional Lie algebra and a Cartan subalgebra and showed that the latter is not closed under composition or Lie bracket; however, it is a commutative, associative algebra.

TL;DR: Exploiting links between the algebraic geometry over groups and model theory the authors solve two problems on geometrical equivalence of groups which are due to B. Plotkin.

TL;DR: In this article, a functor associated with Alexander duality provides a duality on the level of free and injective resolutions, and numerous Bass and Betti number relations result as corollaries.

TL;DR: In this paper, the inequality between the multiplicity and the colength of the tight closure of parameter ideals was investigated, and it was shown that the inequality is not the same as the usual inequality between multiplicities and colength.

TL;DR: In this paper, the authors classified "quadratic" conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov super-algebra.

TL;DR: In this paper, the polynomial ring over which is not a nil algebra is constructed, which answers a question of Amitsur, and it is shown that it is a polynomial algebra over a countable field.

TL;DR: In this article, Nikshych et al. derived two numerical invariants for weak C *-Hopf algebras of trivial hypercenter, which are the common indices I and δ, respectively, of the Haar, respectively Markov, conditional expectations of either one of the inclusions A L/R ǫ⊂ A or A Rǫ/ǫǫ⁡ǫ ⁡⁠ǫ for both inclusions.

TL;DR: In this article, the authors developed the theory of generalized triangular matrix representation in an abstract setting, which is accomplished by introducing the concept of a set of left triangulating idempotents.

TL;DR: In this article, a field theory for the extension k(C)/k(P 1) of a smooth plane quartic curve over a rational function field is presented. But the authors do not consider the Galois closure of the extension.

TL;DR: In this article, the authors investigated the existence of primitive permutation groups with a transitive subgroup containing no nontrivial subnormal subgroup and showed that such primitive groups are rather rare and that their existence is intimately connected with factorisations of almost simple groups.

TL;DR: In this paper, a general construction for pointed co-Frobenius Hopf algebras is presented, and some classification results for the examples obtained are given for some examples.

TL;DR: In this paper, the authors present counterexamples to four conjectures which appeared in the literature in com-mutative algebra and algebraic geometry. The four questions are largely unrelated, and yet their answers are connected by a common thread: they are combina-torial in nature, involving monomial ideals and binomial ideals, and they were found by exhaustive computer search using the symbolic algebra systems Maple and Macaulay 2.

TL;DR: By counting the number of isomorphism classes of representations of quivers over finite fields with fixed dimension vectors, the authors obtained a multi-variable formal identity, which turns out to be a q-analogue of the Kac denominator identity modulus.

TL;DR: In this article, the Hochschild homology and cohomology groups of the invariant algebra A n (C ) G were computed for a finite subgroup of Sp (2 n, C ) acting by automorphisms in the Weyl algebra.

TL;DR: The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises and in subjects as diverse as optimization, coding theory, theta functions, and recently in our proof that certain general sets of objects fail to satisfy the minimal free resolution conjecture as mentioned in this paper.

TL;DR: In this article, the authors classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional locally finite Abelian derivation subalgebra such that the algebra is derivation-simple.

TL;DR: In this paper, the concept of the characteristic tilting module and of the Ringel dual for quasi-hereditary algebras is generalized for the setting of standardly stratified algesbras.

TL;DR: In this paper, the authors studied the structure of the partial group algebra K par (G) where G is a finite group and showed that if the characteristic of K does not divide the order of G 1, then K par(G 1 ) is isomorphic to G 2 if and only if G 1 is isomorphized to G2.

TL;DR: Benkart and Roby as mentioned in this paper showed that the down-up algebras of G Benkart (1998, in “Recent Progress in Algebra,” Contemporary Mathematics Vol 224, Am Math Soc, Providence) lie in a certain class of iterated skew polynomial rings, called ambiskew polynometric rings, in which two indeterminates x and y over a commutative ring B involve the same endomorphism σ of B, but from different sides, that is, yb = ǫσ(b)

TL;DR: In this article, it was shown that both K(V) and K(P(V)) are rational ( = purely transcendental) over K. Similar results hold for a cyclic affine action.

TL;DR: In this article, the structure and classification of finite modules over codimension two local complete intersections are analyzed from the point of view of differential graded homological algebra over a Koszul complex that resolves R over Q.

TL;DR: In this paper, a freeness result for Nichols subalgebras over certain Nichols subals was proved, which allows us to classify pointed Hopf algebra of prime and prime squared index.

TL;DR: In this paper, a generalization of the Terwilliger algebra is proposed, which is the associative C -algebra with identity generated by a given Bose Mesner algebra M and the associated dual M* with a pair of dual character algebras C and C*.