共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
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
3.
We show that the symplectic groups PSp6(q) are Hurwitz for all q = p m ≥ 5, with p an odd prime. The result cannot be improved since, for q even and q = 3, it is known that PSp6(q) is not Hurwitz. In particular, n = 6 turns out to be the smallest degree for which a family of classical simple groups of degree n, over 𝔽 p m , contains Hurwitz groups for infinitely many values of m. This fact, for a given (possibly large) p, also follows from [9] and [10]. 相似文献
4.
David Easdown 《代数通讯》2013,41(8):3518-3537
The minimal faithful permutation degree μ(G) of a finite group G is the least nonnegative integer n such that G embeds in the symmetric group Sym(n). Clearly μ(G × H) ≤ μ(G) + μ(H) for all finite groups G and H. In 1975, Wright ([10]) proved that equality occurs when G and H are nilpotent and exhibited an example of strict inequality where G × H embeds in Sym(15). In 2010 Saunders ([7]) produced an infinite family of examples of permutation groups G and H where μ(G × H) < μ(G) + μ(H), including the example of Wright's as a special case. The smallest groups in Saunders’ class embed in Sym(10). In this article, we prove that 10 is minimal in the sense that μ(G × H) = μ(G) + μ(H) for all groups G and H such that μ(G × H) ≤9. 相似文献
5.
Vyacheslav Futorny 《代数通讯》2013,41(8):3381-3385
In this note we extend the results of Bekkert and Futorny in [2] and Hemmer, Kujawa and Nakano in [10] and determine the derived representation type of Schur superalgebras. 相似文献
6.
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
7.
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
8.
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
9.
We show that π-regular rings and clean rings can be completely characterized by topological properties of their prime spectrums respectively. In addition, we give some applications of those result. Among others, we improve the main result of Samei (2004) and give a new criterion for a clean ring that a commutative ring is clean if and only if idempotents lifts modulo every radical ideal. 相似文献
10.
Samuel M. Corson 《代数通讯》2018,46(10):4317-4324
In this note we strengthen a result of Newman and use it to prove a conjecture of Nakamura stated in [10] that torsion-free one-relator groups are noncommutatively slender. 相似文献
11.
12.
13.
14.
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
15.
16.
Gustavo A. Fernández-Alcober 《代数通讯》2013,41(11):3928-3942
Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. We obtain two new lower bounds for ν(G) when G is a non-abelian finite p-group and p is odd. More precisely, if |G| =p n , exp Z(G) = p e , and exp G/G′ =p f , let us define λ(G) = n ? e and κ(G) = n ? f. Then we prove that ν(G) ≥ p(λ(G) ?3) +2 and ν(G) ≥ p(κ(G) ?3) +2. The first bound improves the bound ν(G) ≥ λ(G) ?1 given by [10], and almost in every case, the second one improves the bound ν(G) ≥ p(k ? 1) +1 obtained by [6], where k is defined by the condition that |G′| =p k . 相似文献
17.
Qingjie Cao Sergey Piskarev Stefan Siegmund 《Numerical Functional Analysis & Optimization》2013,34(10):1287-1307
This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u 0, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10, 11]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value problems with exponential bounded solutions on the corresponding subspaces. We show that such a decomposition of the flow persists under rather general approximation schemes, utilizing a uniform condensing property. The main assumption of our results are naturally satisfied, in particular, for operators with compact resolvents and condensing semigroups and can be verified for finite elements as well as finite differences methods. 相似文献
18.
In (2009), Towers [10] presented the notion of c-ideality of a subalgebra of a Lie algebra, and gave some characterizations of solvable and supersolvable Lie algebras. In this article, we further investigate the influence of c-ideality of some subalgebras on the structure of Lie algebras. We also obtain some equivalent conditions for supersolvability of a finite dimensional Lie algebra. 相似文献
19.
Joan F. Tent 《代数通讯》2013,41(11):4025-4032
Let G be a p-solvable group of p-length l, where p is any prime. We show that G has at least 2 l irreducible characters of degree coprime to p and having values inside ? p . This generalizes a previous result for p = 2 [6] to arbitrary primes. With the same notation, we prove that if p is odd then G has at least 2 l Galois orbits of conjugacy classes of p-elements having values in ? p . 相似文献
20.
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