共查询到20条相似文献,搜索用时 62 毫秒
1.
Zenghui Gao 《代数通讯》2013,41(8):3035-3044
This article continues to investigate a particular case of Gorenstein FP-injective modules, called strongly Gorenstein FP-injective modules. Some examples are given to show that strongly Gorenstein FP-injective modules lie strictly between FP-injective modules and Gorenstein FP-injective modules. Various results are developed, many extending known results in [1]. We also characterize FC rings in terms of strongly Gorenstein FP-injective, projective, and flat modules. 相似文献
2.
Ladislav Bican 《代数通讯》2013,41(11):4098-4103
It is well-known (see [13]) that a hereditary torsion theory τ for the category R-mod is noetherian if and only if the class of all τ-torsionfree τ-injective modules is closed under arbitrary direct sums. So, it is natural to investigate the hereditary torsion theories having the property that the class of all τ-torsionfree injective modules is closed under arbitrary direct sums, which are called ?-noetherian. These torsion theories have been studied by Teply in [16]. In the second part of this note we shall study the weakly exact hereditary torsion theories, which generalize the exact one's. 相似文献
3.
4.
Anders O. F. Hendrickson 《代数通讯》2013,41(12):4420-4438
Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain approximations to the ordinary character theory of the group [7]. We make explicit the connection between supercharacter theories and Schur rings, and we provide supercharacter theory constructions which correspond to Schur ring products of Leung and Man [12], Hirasaka and Muzychuk [10], and Tamaschke [20]. 相似文献
5.
Over a commutative ring R, a module is artinian if and only if it is a Loewy module with finite Loewy invariants [5]. In this paper, we show that this is not necesarily true for modules over noncommutative rings R, though every artinian module is always a Loewy module with finite Loewy invariants. We prove that every Loewy module with finite Loewy invariants has a semilocal endomorphism ring, thus generalizing a result proved by Camps and Dicks for artinian modules [3]. Finally, we obtain similar results for the dual class of max modules. 相似文献
6.
A new family of non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation is constructed. Two subfamilies, consisting of irretractable square-free solutions, are new counterexamples to Gateva-Ivanova’s Strong Conjecture [7]. They are in addition to those obtained by Vendramin [15] and [1]. 相似文献
7.
The article considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter example of Serrin [18], it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia [19] and Boccardo-Galouët [4] and the two notions of solutions of [2, 7], and show that they are equivalent. As side results, we reformulate the solution in the sense of [19], and prove the existence of solutions in the sense of [2, 4, 7] in case of mixed boundary conditions. 相似文献
8.
9.
In this article, we provide a semilocal analysis for the Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting using recurrence relations. Numerical examples to validate our main results are also provided in this study to show that STTM is faster than other methods ([7, 13]) using similar convergence conditions. 相似文献
10.
It is well known that every serial Noetherian ring satisfies the restricted minimum condition. In particular, following Warfield (1975), such a ring is a direct sum of an Artinian ring and hereditary prime rings. The aim of this note is to show that every serial ring having the restricted minimum condition is Noetherian. 相似文献
11.
Álvaro Muñoz 《代数通讯》2018,46(9):3873-3888
In this paper we give a complete classification of pointed fusion categories over ? of global dimension 8. We first classify the equivalence classes of pointed fusion categories of dimension 8, and then we proceed to determine which of these equivalence classes have equivalent categories of modules following the procedure presented in [9, 11]. The results of this paper permit to recover the classification of twisted quantum doubles of groups of order 8 up to gauge equivalence of braided quasi-Hopf algebras that was previously done in [6] and [5]. 相似文献
12.
Local Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in [5]. In this paper we extend the notion of local Weyl modules for a Lie algebra 𝔤 ?A, where 𝔤 is any Kac–Moody algebra and A is any finitely generated commutative associative algebra with unit over ?, and prove a tensor product decomposition theorem which generalizes result in [2, 5]. 相似文献
13.
Tokuji Araya 《代数通讯》2013,41(7):3038-3052
In this article, we study reflexive subcategories of the category of finitely generated modules over Cohen–Macaulay local rings R. One of the main results yields a complete classification of the reflexive subcategories for the case when R is a one-dimensional complete local hypersurface of finite Cohen–Macaulay representation type. The other result yields a one-to-one correspondence between the subclasses of a stable category and the reflexive subcategories over a complete local hypersurface. Then, we attempt to extend the result in Takahashi [8, Proposition 4.4] to a reflexive subcategory. 相似文献
14.
In the very influential paper [4] Caffarelli and Silvestre studied regularity of (?Δ)s, 0<s<1, by identifying fractional powers with a certain Dirichlet-to-Neumann operator. Stinga and Torrea [15] and Galé et al. [7] gave several more abstract versions of this extension procedure. The purpose of this paper is to study precise regularity properties of the Dirichlet and the Neumann problem in Hilbert spaces. Then the Dirichlet-to-Neumann operator becomes an isomorphism between interpolation spaces and its part in the underlying Hilbert space is exactly the fractional power. 相似文献
15.
Huanyin Chen 《代数通讯》2013,41(4):1352-1362
An element of a ring is called strongly J-clean provided that it can be written as the sum of an idempotent and an element in its Jacobson radical that commute. We investigate, in this article, a single strongly J-clean 2 × 2 matrix over a noncommutative local ring. The criteria on strong J-cleanness of 2 × 2 matrices in terms of a quadratic equation are given. These extend the corresponding results in [8, Theorems 2.7 and 3.2], [9, Theorem 2.6], and [11, Theorem 7]. 相似文献
16.
V. V. Bavula 《代数通讯》2013,41(4):1381-1406
ABSTRACT In Dixmier (1968), the author posed six problems for the Weyl algebra A 1 over a field K of characteristic zero. Problems 3, 6, and 5 were solved respectively by Joseph (1975) and Bavula (2005a). Problems 1, 2, and 4 are still open. In this article a short proof is given to Dixmier's problem 6 for the ring of differential operators 𝒟 (X) on a smooth irreducible algebraic curve X. It is proven that, for a given maximal commutative subalgebra C of 𝒟 (X), (almost) all noncentral elements of it have the same type, more precisely, have exactly one of the following types: (i) strongly nilpotent; (ii) weakly nilpotent; (iii) generic; (iv) generic, except for a subset K*a + K of strongly semi-simple elements; (iv) generic, except for a subset K*a + K of weakly semi-simple elements, where K* := K\{0}. The same results are true for other popular algebras. 相似文献
17.
18.
ABSTRACT Model theorists have made use of low-dimensional continuous cohomology of infinite permutation groups on profinite modules, see Ahlbrandt and Ziegler (1991), Evans (1997b), Evans et al. (1997), and Hodges and Pillay (1994), for example. We expand the module category in order to widen the cohomological toolkit. For an important class of groups we use these tools to establish criteria for finiteness of cohomology. 相似文献
19.
John Talboom 《代数通讯》2013,41(4):1795-1808
This article investigates the irreducibility of certain representations for the Lie algebra of divergence zero vector fields on a torus. In [2] Rao constructs modules for the Lie algebra of polynomial vector fields on an N-dimensional torus, and determines the conditions for irreducibility. The current article considers the restriction of these modules to the subalgebra of divergence zero vector fields. It is shown here that Rao's results transfer to similar irreducibility conditions for the Lie algebra of divergence zero vector fields. 相似文献
20.
Michael Hellus 《代数通讯》2013,41(7):2615-2621
In continuation of [1] we study associated primes of Matlis duals of local cohomology modules (MDLCM). We combine ideas from Helmut Zöschinger on coassociated primes of arbitrary modules with results from [1 4-6], and obtain partial answers to questions which were left open in [1]. These partial answers give further support for conjecture (*) from [1] on the set of associated primes of MDLCMs. In addition, and also inspired by ideas from Zöschinger, we prove some non-finiteness results of local cohomology. 相似文献