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1.
It is known that the semigroup Sing n of all singular self-maps of X n = {1,2,…, n} has rank n(n ? 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing n , has the same value as the rank. (See Gomes and Howie, 1987.) Idempotents generating Sing n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ay\i k et al. (2005). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing n , defined as the smallest number of (m, r)-path-cycles generating Sing n , is once again n(n ? 1)/2. 相似文献
2.
In this paper, based on the results in [8] we give a monomial basis for q-Schur superalgebra and then a presentation for it. The presentation is different from that in [12]. Imitating [3] and [7], we define the infinitesimal and the little q-Schur superalgebras. We give a “weight idempotent presentation” for infinitesimal q-Schur superalgebras. The BLM bases and monomial bases of little q-Schur superalgebras are obtained, and dimension formulas of infinitesimal and little q-Schur superalgebras are deduced. 相似文献
3.
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
4.
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
5.
Daniel Larsson 《代数通讯》2013,41(12):4303-4318
In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) to the simple 3-dimensional Lie algebra 𝔰𝔩2(𝔽). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to 𝔰𝔩2(𝔽) we can, by choosing parameters suitably, deform 𝔰𝔩2(𝔽) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where 𝔰𝔩2(𝔽) is rigid. 相似文献
6.
A semigroup S is called F-monoid if S has an identity and if there exists a group congruence ρ on S such that each ρ-class of S contains a greatest element with respect to the natural partial order of S (see Mitsch, 1986). Generalizing results given in Giraldes et al. (2004) and specializing some of Giraldes et al. (Submitted) five characterizations of such monoids S are provided. Three unary operations “?”, “○”, and “ ? ” on S defined by means of the greatest elements in the different ρ-classes of S are studied. Using their properties a charaterization of F-monoids S by their regular part S° = {a°|a ? S} and the associates of elements in S° is given. Under the hypothesis that S ? = {a ?|a ? S} is a subsemigroup it is shown that S is regular, whence of a known structure (see Giraldes et al., 2004). 相似文献
7.
Motivated by the construction of new examples of Artin–Schelter regular algebras of global dimension four, Zhang and Zhang [6] introduced an algebra extension A P [y 1, y 2; σ, δ, τ] of A, which they called a double Ore extension. This construction seems to be similar to that of a two-step iterated Ore extension over A. The aim of this article is to describe those double Ore extensions which can be presented as iterated Ore extensions of the form A[y 1; σ1, δ1][y 2; σ2, δ2]. We also give partial answers to some questions posed in Zhang and Zhang [6]. 相似文献
8.
Mi Hee Park 《代数通讯》2013,41(4):1280-1292
Let R be an integral domain. A w-ideal I of R is called a w-multiplicative canonical ideal if (I: (I: J)) = J for each w-ideal J of R. In particular, if R is a w-multiplicative canonical ideal of R, then R is a w-divisorial domain. These are the w-analogues of the concepts of a multiplicative canonical ideal and a divisorial domain, respectively. Motivated by the articles [8, 10], we study the domains possessing w-multiplicative canonical ideals; in particular, we consider Prüfer v-multiplication domains. 相似文献
9.
Michel Gros 《代数通讯》2013,41(5):2163-2170
Soit p un nombre premier. Nous établissons l'existence de neutralisations de divers complétés de l'algèbre de Weyl quantique spécialisée en une racine de l'unité primitive d'ordre p (qui est “génériquement” une algèbre d'Azumaya) et donnons en particulier un énoncé de neutralisation explicite relevant celui construit en caractéristique p dans [3]. Let p be a prime number. We establish the existence of neutralizations of various completions of the quantum Weyl algebra specialized at a primitive root of unity of prime order p (which is “generically” an Azumaya algebra) and, in particular, we give a statement of explicit neutralization similar to the one built in characteristic p in [3]. 相似文献
10.
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
11.
Zhixiang Wu 《代数通讯》2013,41(9):3869-3897
In the present article, we introduce G-graded left symmetric H-pseudoalgebras, where G is a grading group, and H is a cocommutative Hopf algebra. Some results about associative H-pseudoalgebras in [23] are generalized. The commutator algebras of the G-graded left symmetric H-pseudo-algebras are Lie H-pseudoalgebras, which are classified when the grading group is trivial in [3]. We investigate the left symmetric structure of Lie H-pseudoalgebras W(𝔟), S(𝔟), and He defined in [3]. 相似文献
12.
Let ξ = (p 1, p 2,…) be a given infinite sequence of not necessarily distinct primes. In 1976, the structure of locally finite groups S(ξ) (respectively A(ξ) ) which are obtained as a direct limit of finite symmetric (finite alternating) groups are investigated in [7]. The countable locally finite groups A(ξ) gives an important class in the theory of infinite simple locally finite groups. The classification of these groups using the lattice of Steinitz numbers is completed by Kroshko and Sushchansky in 1998 see [8]. Here we extend the results on the structure of centralizers of elements to centralizers of arbitrary finite subgroups and correct some of the errors in the section of centralizers of elements in [8]. We construct for each infinite cardinal κ, a new class of uncountably many simple locally finite groups of cardinality κ as a direct limit of finitary symmetric groups. We investigate the centralizers of elements and finite subgroups in this new class of simple locally finite groups, and finally, we characterize this class by the lattice isomorphism with the cardinality of the group and the Steinitz numbers. 相似文献
13.
Francesc Bars 《代数通讯》2013,41(6):2160-2170
We determine the group structure of the normalizer of Γ0(N) in SL 2(?) modulo Γ0(N). These results correct the Atkin–Lehner statement (Atkin and Lehner, 1970, Theorem 8). 相似文献
14.
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
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.
This article provides in the setting of infinite dimensional Hilbert space, a result concerning the existence and uniqueness of solutions for Lipschitz single-valued perturbations of evolution problems associated with time-dependent subdifferential operators. The result is used to extend to optimal control problems associated with such equations the relaxation theorems with Young measures established in Casting et al. [7, 11] and Edmond and Thibault [11]. 相似文献
17.
We complement two papers on supertropical valuation theory ([11], [12]) by providing natural examples of m-valuations (= monoid valuations), and afterwards of supervaluations and transmissions between them. These supervaluations have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. We develop the basics of the theory of such semirings and transmissions. 相似文献
18.
Katsiaryna Krupchyk 《偏微分方程通讯》2015,40(3):438-474
We prove uniform Lp estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding result of [3] in the case of Laplace-Beltrami operators on Riemannian manifolds. In doing so, we follow the methods, developed in [1] very closely. We also show that spectral regions in our Lp resolvent estimates are optimal. 相似文献
19.
John Bradley 《代数通讯》2013,41(8):2588-2599
A group is 2-generated if it can be generated by two elements x and y. In this case y is called a mate for x. Brenner and Wiegold (1975a) defined a finite group G to have spread r if for every set {x 1, x 2,…, x r } of distinct nontrivial elements of G, there exists an element y ? G such that G = 〈 x i , y〉 for all i. A group is said to have exact spread r if it has spread r but not r + 1. The exact spread of a group G is denoted by s(G). Ganief (1996) in his Ph.D. thesis proved that if G is a sporadic simple group, then s(G) ≥ 2. In Ganief and Moori (2001) the second author and Ganief used probabilistic methods and established a reasonable lower bound for the exact spread s(G) of each sporadic simple group G. The present article deals with the search for reasonable upper bounds for the exact spread of the sporadic simple groups. 相似文献
20.
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