Showing papers in "Journal of Pure and Applied Algebra in 2003"

TL;DR: Weak monoidal Morita equivalence of tensor categories, denoted A ≈ B, has been studied in this article, where it has been shown that A and B have equivalent quantum doubles (centers) and (if A, B are semisimple spherical or ∗ -categories) have equal dimensions and give rise the same state sum invariant of closed oriented 3-manifolds as recently defined by Barrett and Westbury.

TL;DR: In this article, a generalization of this result to the quantum double of more general tensor categories is presented. But the results are restricted to the case where the objects of the braided tensor category Z (C ) are simple objects.

TL;DR: For a commutative ring R with set of zero-divisors Z (R), the zero-Divisor graph of R is Γ( R ) = Z ( R )−{0), with distinct vertices x and y adjacent if and only if xy = 0 as mentioned in this paper.

TL;DR: In this paper, the lattice of subvarieties of BL-algebras is described in terms of ordinal sums of Wajsberg hoops, and a characterization of generic BL algebra that generate the whole variety is given.

TL;DR: It is claimed that a deep mathematical theory is needed to make progress in complexity theory, and considers logical gates as generators for some algebraic structure with two compositions and interested in the relations satisfied by those generators.

TL;DR: A ring R is called reversible if ab = 0 implies ba = 0 for a, b ∈ R, where b is the right quotient ring of R and ab is a positive integer.

TL;DR: In this article, a functoriality property of the virtual fundamental class on the moduli of stable maps is proven, which is used to supply a proof of a conjecture of Cox, Katz and Lee.

TL;DR: In this article, the lower bounds for Betti numbers of the rack, quandle and degeneracy cohomology given in Carter et al. (J. Pure Appl. Algebra, 157 (2001) 135) are in fact equalities.

TL;DR: In this article, a quandle cohomology group of the form Z p [T,T −1 ]/(T−ω) for any finite Alexander quandles over a finite field is given.

TL;DR: For a symmetric monoidal-closed category V and a suitable monad T on the category of sets, this paper introduced the notion of reflexive and transitive (T, V ) -algebra and showed that various old and new structures are instances of such algebras.

TL;DR: In this article, it was shown that if the rank of the root system is at least 2 and the Bass-Serre dimension of the commutative ring is finite, then the quotient G ( Φ, R )/E( Φ, R ) is nilpotent by abelian.

TL;DR: The lower bounds for Betti numbers given in (J. Pure Appl. Algebra 157 (2001) 135) are equalities for a class of racks that includes dihedral and Alexander racks as discussed by the authors.

TL;DR: In this article, a subgroup A of a finite group G is called a CAP -subgroup of G if for any chief factor H/K of G, we have H ∩A=K∩A or HA=KA.

TL;DR: In this article, it was shown that if Froberg's conjecture on the Hilbert function is true then any such redundant terms in the minimal free resolution must occur in the top two possible degrees of the free module.

TL;DR: In this paper, it was shown that H2(QK) = Z p, where p is the number of prime summands in a connected sum decomposition of a knot K in the 3-sphere.

TL;DR: The classical 3×3 lemma holds in any regular protomodular category C with a zero object as mentioned in this paper, and it is investigated whether there is a denormalized version when the category no longer has zero objects, as, for instance, any slice category C /X of the category C, or any slice categories of an abelian category.

TL;DR: In this article, a version of the classical Dold-Thom theorem for the RO(G )-graded equivariant homology functors H ∗ G (−; M ), where G is a finite group, M is a discrete Z [G] -module, and M is the Mackey functor associated to M, was proved.

TL;DR: In this paper, it was shown that the category of unbounded complexes of sheaves on a topological space has enough K-injective complexes for a triangulated category of equivariant motives.

TL;DR: In this article, the authors develop group extension theory over an o-minimal structure N and use it to describe N -definable solvable groups, and prove an ominimal analogue of the Lie-Kolchin-Mal'cev theorem.

TL;DR: In this paper, the authors generalize Northcott's inequality on Hilbert coefficients of I given in Northcott (J. London Math. Soc. 35 (1960) 209), without assuming that A is a Cohen-Macaulay ring.

TL;DR: In this paper, the irreducibility of Verma modules over the generalized Virasoro algebra Vir[G] has been shown to be irrevocable for any c,h ∈ F.

TL;DR: In this paper, the authors derive Tannaka duality between right adjoint strong monoidal functors and opmonoidal monads by treating such monads as abstract "quantum groupoids".

TL;DR: In this paper, an etale descent formula for topological Hochschild homology and a HKR theorem for smooth S-algebras were derived and proved for topologically topological topological homology.

TL;DR: In this article, the Hilbert-Samuel function of a generic standard graded K-algebra K[X 1,…,X n ]/(g 1,..,g m ) was studied for the degree-reverse-lexicographic order.

TL;DR: Substitudes as mentioned in this paper generalize both monoidal enriched categories and operads, and are a little more general than multicategories, and can bear braidings and symmetries.

TL;DR: In this paper, it was shown that for every finite subset F of R, the semialgebraic set R"\F is a polynomial image of R; and for any independent linear form 1, of R", the semi-gebraic subset of R" ∈ {l(1) > 0,..., l(r)> 0} subset of a linear form of R ∈ [1] is a Polynomial Image of R.

TL;DR: In this paper, it was shown that similar ideas work in the multivariable case over rings (instead of elds) and that the notion of recursiveness is exactly the same for the case of anite number of noncommuting variables over a eld.

TL;DR: In this paper, Lepowsky et al. introduced graded q-traces associated to vertex operator algebra and superalgebras, which they refer to as n -point functions.

TL;DR: In this paper, the locally nilpotent derivations of the k -algebra B = k [X 1,X 2,Y]/(ϕ−X 1 X 2 ), where k is a field of characteristic zero, X1,X2,Y are indeterminates over k and ϕ∈ k [Y] is a nonconstant polynomial.

TL;DR: In this paper, the authors studied projective objects in the category O c of the rational Cherednik algebra introduced by Berest, Etingof and Ginzburg, and proved that it has enough projectives and that it is a highest weight category in the sense of Cline, Parshall and Scott, and therefore satisfies an analog of the BGG-reciprocity formula for a semisimple Lie algebra.