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Showing papers in "Journal of Algebra in 2013"


Journal ArticleDOI
TL;DR: In this paper, a general theory based on idempotents and direct sum decompositions was developed to unify several variations of the notions of clean and strongly clean, and a new class of clean rings was investigated.

179 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied algebraic properties of the ideals defining star configurations, including partial results about Hilbert functions, generators and minimal free resolutions of ideals and their symbolic powers.

111 citations


Journal ArticleDOI
TL;DR: In this paper, the authors introduce compatible bimodules, a class of A-B-bimodule that is compatible with the projective modules over algebra Λ = AM0B.

93 citations


Journal ArticleDOI
TL;DR: Barucci and Froberg as mentioned in this paper introduced the notion of an almost Gorenstein ring in the case of an analytically unramified local ring (R, m ) and provided a framework that allows us to generalize this notion to include the analytical ramified case.

92 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that there is in general no containment I ( 3 ) ⊂ I 2 for an ideal I of points in P 2, which answers in the negative a question asked by Huneke and generalized by Harbourne.

88 citations


Journal ArticleDOI
TL;DR: The notion of hom-Lie 2-algebras has been introduced in this paper, which is the hom-analogues of the string Lie 2-Algebra associated to any semisimple involutive hom-lie alga.

88 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that local uniformization of algebraic varieties is always possible after a purely inseparable extension of the field of rational functions, and therefore any valuation can be uniformized by a purely irreproducible alteration.

78 citations


Journal ArticleDOI
TL;DR: It is proved that in a large majority of cases there exists a transfer homomorphism to a monoid of zero-sum sequences over a ray class group of O, which implies that all the structural finiteness results for sets of lengths hold also true for R.

72 citations


Journal ArticleDOI
TL;DR: In this article, the stability of the Gorenstein category G (C ) has been shown to be closed under direct summands under the assumption that the G(C ) -dimension of an object in A is known.

71 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that a prime right nonsingular ring R is self-injective if RR is invariant under automorphisms of its injective hull.

67 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the diameter of the commuting graph of a finite group with trivial center and showed that the connected components of the graph have diameter at most 10.5.

Journal ArticleDOI
TL;DR: In this article, the authors define and study representations of quantum toroidal gl n with natural bases labeled by plane partitions with various conditions, and give an explicit description of a family of highest weight representations for quantum affine gl n.

Journal ArticleDOI
TL;DR: In this paper, the primitive prime ideals of the Leavitt path algebra L K (E ) were characterized in terms of their generators and necessary and sufficient conditions on the graph E under which every prime ideal of L K(E ) is primitive.

Journal ArticleDOI
TL;DR: In this paper, it was shown that any smooth arithmetically Gorenstein surface whose rank-r Ulrich bundles admit a generalized theta-divisor admits del Pezzo surfaces.

Journal ArticleDOI
TL;DR: In this paper, Niroom and Niroom et al. classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one.

Journal ArticleDOI
TL;DR: This paper identifies each cluster variable with its snake graph, and interpret relations among the cluster variables in terms of these graphs, and gives a new proof of skein relations of two cluster variables.

Journal ArticleDOI
TL;DR: In this paper, the authors outline the structure of the category of the Gorenstein projective Λ-modules, where Λ is a Nakayama algebra, and introduce the resolution quiver of Λ.

Journal ArticleDOI
TL;DR: In this paper, it was shown that a module invariant under automorphisms of its injective hull satisfies the exchange property and that automorphism-invariant modules are clean.

Journal ArticleDOI
TL;DR: A Waring decomposition is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible as mentioned in this paper, and it is known that any Waring-decomposition of a monomial can be obtained from a complete intersection ideal.

Journal ArticleDOI
Kenta Ueyama1
TL;DR: In this article, the authors define a notion of noncommutative graded isolated singularity, and study AS-Gorenstein isolated singularities and the categories of graded maximal Cohen-Macaulay modules over them.

Journal ArticleDOI
TL;DR: In this article, it was shown that every Picard rank one smooth Fano threefold has a weak Landau-Ginzburg model coming from a toric degeneration, which can be compactified to K3 surfaces with Picard lattice of rank 19.

Journal ArticleDOI
TL;DR: In this article, structural pre-braidings characterizing different algebraic structures: a rack, an associative algebra, a Leibniz algebra and their representations are constructed.

Journal ArticleDOI
TL;DR: In this article, a tensor product of a finite number of irreducible Virasoro modules of the form Ω ( λ i, a i ) was obtained.

Journal ArticleDOI
TL;DR: In this article, the authors considered traces on module categories over pivotal fusion categories which are compatible with the module structure and showed that such traces characterise the Morita classes of special haploid Frobenius algebras.

Journal ArticleDOI
TL;DR: In this paper, the Auslander-Reiten duality theorem was extended to local rings of positive depth, and it was shown that the duality holds over local rings with positive depth.

Journal ArticleDOI
TL;DR: In this paper, the necessary and sufficient conditions for fraction modules to be irreducible are determined, and the necessary conditions for two isomorphic fraction modules over centerless Virasoro algebra V to be isomorphic.

Journal ArticleDOI
TL;DR: In this paper, an evolution algebra of the bisexual population is introduced, which identifies the coefficients of inheritance of a bisexual population as the structure constants of the algebra and proves that the algebra is commutative, not associative and not necessarily power-associative.

Journal ArticleDOI
TL;DR: In this paper, the second radical of a module over an arbitrary ring R is defined as the dual notion of the prime radical of the module and the notion of m-systems is introduced.

Journal ArticleDOI
TL;DR: In this paper, Chen and Sun showed that singular equivalence of Morita type has some bi-joint functor properties and preserves positive degree Hochschild homology under some conditions.

Journal ArticleDOI
TL;DR: In this paper, a large class of simple modules for the Heisenberg-Virasoro algebra is constructed, which are determined by the simple modules over the finite-dimensional quotient algebras of certain natural subalgebra.