共查询到20条相似文献,搜索用时 31 毫秒
1.
《代数通讯》2013,41(10):4945-4963
ABSTRACT We give another proof of Harrison's decomposition result,[2] Prop. 2.3 for higher degree forms over a noetherian ring, exploiting an earlier introduction of the centre. We generalise to higher degree forms over a noetherian scheme: we extend the notion of centre; we prove a decomposition result; we extend Harrison's result,[2] Prop. 4.3 on the behaviour of the centre under a flat base extension; and we improve his result,[2] Prop. 4.2, giving conditions on the base scheme under which the centre of the tensor product of two higher degree forms is isomorphic to the tensor product of their centres. 相似文献
2.
《代数通讯》2013,41(6):3001-3020
Abstract Let L be a positive definite even lattice and let g ∈ Aut L be a fixed point free automorphism of order 3. We determine the twisted Zhu's algebra A ? (V L ) for the lattice vertex operator algebra V L , where ? is an automorphism of V L induced from g. As a result, we show that the set of all irreducible ?-twisted modules for V L (up to isomorphism) are exactly those constructed by Dong and Lepowsky (1996) and Lepowsky (1985). 相似文献
3.
《代数通讯》2013,41(6):3037-3043
ABSTRACT In his recent work, [1] and [2], on the pure semisimplicity conjecture Simson raised two problems about the structure of the direct sum decomposition of the direct product modulo the direct sum of indecomposable preinjective modules over right pure semisimple hereditary rings. The main goal of this paper is the proof of a theorem that resolves one of these problems and provides a partial answer to the other. 相似文献
4.
《代数通讯》2013,41(10):4621-4627
ABSTRACT In this note we show that the hermitian level of a quaternion division algebra with involution of second kind, is always a power of 2, when it is finite. This result holds for a field with trivial or non-trivial involution, and quaternion division algebras with involution of first kind [6], [5], [9]. 相似文献
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《代数通讯》2013,41(4):1765-1775
Abstract This paper studies two homogenizations of the down-up algebras introduced in Benkart and Roby (Benkart, G., Roby, T. (1998). Down-up Algebras. J. Algebra 209:305–344). We show that in all cases the homogenizing variable is not a zero-divisor, and that when the parameter β is non-zero, the homogenized down-up algebra is a Noetherian domain and a maximal order, and also Artin-Schelter regular, Auslander regular, and Cohen-Macaulay. We show that all homogenized down-up algebras have global dimension 4 and Gelfand-Kirillov dimension 4, and with one exception all homogenized down-up algebras are prime rings. We also exhibit a basis for homogenized down-up algebras and provide a necessary condition for a Noetherian homogenized down-up algebra to be a Hopf algebra. 相似文献
7.
Enrico Gregorio 《代数通讯》2013,41(4):1137-1146
ABSTRACT In this note,we answer a question of Hong et al. (2003) by proving that if α is a monomorphism of a reduced ring R, and R is α-skew Armendariz, then R is α-rigid. 相似文献
8.
Yi-Ming Zou 《代数通讯》2013,41(5):1529-1540
ABSTRACT Using the local subgroup strategy of An and O'Brien (1997), An and O'Brien (1999), we classify the radical subgroups and chains of the Fischer simple group Fi 22 and verify the Alperin weight conjecture and the Uno reductive conjecture for this group; the latter is a refinement of the Dade reductive and Isaacs–Navarro conjectures. 相似文献
9.
《代数通讯》2013,41(6):2481-2487
In 1989 Nichols and Zoeller [NZ] showed that finite dimensional k-Hopf algebras are free over Hopf subalgebras. An analog result for Yetter Drinfeld Hopf algebras was not known. In this paper the existence of such a basis will be proved. Moreover the existence of a basis in a certain categorial sense cannot be expected. 相似文献
10.
ABSTRACT Let ? be a complete set of Sylow subgroups of a finite group G, that is, ? contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup H of a finite group G is said to be ?-permutable if H permutes with every member of ?. The purpose of this article is to study the influence of ?-permutability of all maximal subgroups of the Sylow subgroups of the generalized Fitting subgroup of some normal subgroup of a finite group G on the structure of G. Our results improve and extend the main results of Asaad (1998), Asaad and Heliel (2003), Asaad et al. (1991), Li et al. (2003), Ramadan (1992), and Srinivasan (1980). 相似文献
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A ring is called clean if every element is a sum of a unit and an idempotent, while a ring is said to be weakly clean if every element is either a sum or a difference of a unit and an idempotent. Commutative weakly clean rings were first discussed by Anderson and Camillo [2] and were extensively investigated by Ahn and Anderson [1], motivated by the work on clean rings. In this paper, weakly clean rings are further discussed with an emphasis on their relations with clean rings. This work shows new interesting connections between weakly clean rings and clean rings. 相似文献
14.
《代数通讯》2013,41(6):2731-2744
In [5] we used functors which are compositions of localization functors to construct sheaves over an arbitrary ring R. These functors share some properties with localization, and questions like when is the composition of localizations a localization functor? arise naturally. In this note we answer this question and some related ones using the key concept of semi-compatibility. 相似文献
15.
《代数通讯》2013,41(9):3179-3193
ABSTRACT If X and Y are sets, we let P(X, Y ) denote the set of all partial transformations from X into Y (that is, all mappings whose domain and range are subsets of X and Y, respectively). We define an operation * on P(X, Y ) by choosing θ ∈ P(Y, X) and writing: α*β = α °θ°β, for each α, β ∈ P(X, Y ). Then (P(X, Y ), *) is a semigroup, and some authors have determined when this is regular (Magill and Subbiah, 1975), when it contains a “proper dense subsemigroup” (Wasanawichit and Kemprasit, 2002) and when it is factorisable (Saengsura, 2001). In this paper, we extend the latter work to certain subsemigroups of (P(X, Y ), *). We also consider the corresponding idea for partial linear transformations from one vector space into another. In this way, we generalise known results for total transformations and for injective partial transformations between sets, and we establish new results for linear transformations between vector spaces. 相似文献
16.
《代数通讯》2013,41(6):2915-2927
ABSTRACT V. B. Styshnev showed in [9] that the existence of n -th roots for a braid is decidable. Garside groups have been introduced in [2] and [3] as a natural proper generalization of Artin groups of finite type. We have to construct a new proof to extend Styshnev's decidability result to Garside groups, as several specific properties of braids used in [9] fail in our case. We show that, under the assumption of a finiteness property of conjugacy, the problem is decidable. 相似文献
17.
《偏微分方程通讯》2013,38(9-10):1685-1704
Abstract The purpose of this article is to prove a sharp bound on the number of resonances for the Laplacian on conformally compact manifolds with constant negative curvature near infinity, thus improving the polynomial bound of Guillopé and Zworki (Guillopé, L., Zworski, M. ([1995b]). Polynomial bound on the number of resonances for some complete spaces of constant negative curvature near infinity. Asympt. Anal. 11:1–22). 相似文献
18.
《代数通讯》2013,41(9):3157-3178
ABSTRACT Pairs (A, L) with A a commutative algebra and L a Lie algebra acting on A by derivations, called Lie algops, are studied as algebraic structures over arbitrary fields of arbitrary characteristic. Lie algops possess modules and tensor products—and are considered with respect to a central simple theory. The simplicity problem of determining the faithful unital simple Lie algops ( A, L ) is of interest since the corresponding Lie algebras AL are usually simple (Jordan, 2000). For locally finite Lie algops, and up to purely inseparable descent, this problem reduces by way of closures to the closed central simplicity problem of determining those which are closed central simple. The simplicity and representation theories for locally nilpotent separably triangulable unital Lie algops are of particular interest because they relate to the problems of classifying simple Lie algebras of Witt type and their representations. Of these, the simplicity theory reduces to that of Jordan Lie algops. The main Theorems 7.3 and 7.4 reduce the simplicity and representation theories for Jordan Lie algops to the simplicity and representation theories for simple nil and toral Lie algops. 相似文献
19.
Thomas Laurent 《偏微分方程通讯》2013,38(12):1941-1964
The purpose of this work is to develop a satisfactory existence theory for a general class of aggregation equations. An aggregation equation is a non-linear, non-local partial differential equation that is a regularization of a backward diffusion process. The non-locality arises via convolution with a potential. Depending on how regular the potential is, we prove either local or global existence for the solutions. Aggregation equations have been used recently to model the dynamics of populations in which the individuals attract each other (Bodnar and Velazquez, 2005; Holm and Putkaradze, 2005; Mogilner and Edelstein-Keshet, 1999; Morale et al., 2005; Topaz and Bertozzi, 2004; Topaz et al., 2006). 相似文献