共查询到20条相似文献,搜索用时 31 毫秒
1.
《代数通讯》2013,41(7):2109-2114
ABSTRACT If M is a simple module over a ring R, then, by Schur's Lemma, its endomorphism ring is a division ring. However, the converse of this property, which we called the CSL property, does not hold in general. The object of this article is to study this converse for a few classes of rings: left Noetherian rings, V-rings and group algebras. First, we establish that a left Noetherian ring R is a CSL ring if and only if a ring R is left–artinian and primary decomposable. Secondly, we prove that a left semiartinian V-ring is CSL. At last, we study the CSL property in group algebra K [ G ] where K a field algebraically closed of characteristic p and G is a finite group of order divisible by p. Our main contribution is that K [ G ] is a CSL ring if and only if Gbf = HP where H is a normal p′-subgroup and bfP a Sylow bfp-subgroup of bfG. In this case, K [ G ] is primary decomposable. 相似文献
2.
《代数通讯》2013,41(9):2899-2920
ABSTRACT Let R be a Noetherian ring and M a finitely generated R -module. In this article, we introduce the set of prime ideals Fnd M , the foundation primes of M . Using the fact that this set is nicely organized by foundation levels, we present an approach to the problem of understanding Annspec M , the annihilator primes of M , via Fnd M . We show: (1) Fnd M is a finite set containing Annspec M . Further, suppose that moreover every ideal of R has a centralizing sequence of generators; now, Annspec M is equal to the set Ass M of associated primes of M. Then: (2) For an arbitrary P ∈ Fnd M , P ∈ Annspec M if and only if there is no Q ∈ Annspec M such that P contains Q , and at the same time, the minimal foundation level on which appears P is greater than the minimal foundation level on which appears Q . 相似文献
3.
For matrices F and G having the same number of rows and the orthogonal projectors P?=?FF ? and Q?=?GG ?, with F ? and G ? denoting the Moore–Penrose inverses of F and G, respectively, several formulae for ranks of various functions of F, G, P and Q are established. Besides a collection of original characterizations, many of which involve the ranks of F*G and (F?:?G) (which coincide with the ranks of PQ and P?+?Q, respectively), some properties known in the literature are reestablished in a generalized form. The variety of relationships considered shows that the approach utilized in the article, based on the partitioned representations of the projectors, provides a powerful tool of wide applicability. 相似文献
4.
ABSTRACT A ring R is called an n-clean (resp. Σ-clean) ring if every element in R is n-clean (resp. Σ-clean). Clean rings are 1-clean and hence are Σ-clean. An example shows that there exists a 2-clean ring that is not clean. This shows that Σ-clean rings are a proper generalization of clean rings. The group ring ?(p) G with G a cyclic group of order 3 is proved to be Σ-clean. The m× m matrix ring M m (R) over an n-clean ring is n-clean, and the m×m (m>1) matrix ring M m (R) over any ring is Σ-clean. Additionally, rings satisfying a weakly unit 1-stable range were introduced. Rings satisfying weakly unit 1-stable range are left-right symmetric and are generalizations of abelian π-regular rings, abelian clean rings, and rings satisfying unit 1-stable range. A ring R satisfies a weakly unit 1-stable range if and only if whenever a 1 R + ˙˙˙ a m R = dR, with m ≥ 2, a 1,…, a m, d ∈ R, there exist u 1 ∈ U(R) and u 2,…, u m ∈ W(R) such that a 1 u 1 + ? a m u m = Rd. 相似文献
5.
Let K be a quasivariety of algebraic systems of finite type. K is said to be universal if the category G of all directed graphs is isomorphic to a full subcategory of K. If an embedding of G may be effected by a functor F:G
K which assigns a finite algebraic system to each finite graph, then K is said to be finite-to-finite universal. K is said to be Q-universal if, for any quasivariety M of finite type, L(M) is a homomorphic image of a sublattice of L(K), where L(M) and L(K) are the lattices of quasivarieties contained in M and K, respectively.?We establish a connection between these two, apparently unrelated, notions by showing that if K is finite-to-finite universal, then K is Q-universal. Using this connection a number of quasivarieties are shown to be Q-universal.
Received February 8, 2000; accepted in final form December 23, 2000. 相似文献
6.
Jingjing Ma 《代数通讯》2013,41(10):3797-3810
An ?-ideal I of a commutative lattice-ordered ring R with positive identity element is called a pure ?-ideal if R = I + ?( x ) for each x ∈ I , where ?(x) is the ?-annihilator of x in R . In this article, we give some results on pure ?-ideals and study the ?-ideal structure of a commutative lattice-ordered ring with positive identity element by using pure ?-ideals. 相似文献
7.
ABSTRACT In this article, we prove that the inner projection of a projective curve with higher linear syzygies has also higher linear syzygies. Specifically, if a very ample line bundle ? on a smooth projective curve X satisfies property N p for p ≥ 1 and H 1 (? ? 2) = 0 , then ?( ? q ) satisfies property N p ? 1 for any point q ∈ X . We also give simple proofs of well-known theorems about syzygies and raise some questions related to the line bundles of degree 2 g which do not satisfy property N 1 . 相似文献
8.
Whaley's Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite
lattices. As a corollary it is shown that every finite lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/3. It is also shown that that every finite modular lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/2, and every finite distributive lattice L with |L|≥4 contains a proper sublattice S with |S|≥3/4|L|.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
Raffaele Mosca 《Graphs and Combinatorics》2001,17(3):517-528
Let G be a graph with n vertices, and denote as γ(G) (as θ(G)) the cardinality of a minimum edge cover (of a minimum clique cover) of G. Let E (let C) be the edge-vertex (the clique-vertex) incidence matrix of G; write then P(E)={x∈ℜ
n
:Ex≤1,x≥0}, P(C)={x∈ℜ
n
:Cx≤1,x≥0}, α
E
(G)=max{1
T
x subject to x∈P(E)}, and α
C
(G)= max{1
T
x subject to x∈P(C)}. In this paper we prove that if α
E
(G)=α
C
(G), then γ(G)=θ(G).
Received: May 20, 1998?Final version received: April 12, 1999 相似文献
10.
W stands for the category of all archimedean l-groups with designated weak unit. The subcategory W
s
of all groups with singular weak unit is analyzed as a full subcategory of W which is both epireflective and monocoreflective. A general technique for "contracting" monoreflections of a category A to a monocoreflective subcategory B is developed and then applied to W
s
to show that: (i) the projectable hull in W
s
is a monoreflection; (ii) essential hulls in W
s
are formed by simply taking the lateral completion, and G is essentially closed in this category if and only if , where X is compact, Hausdorff and extremally disconnected; (iii) the maximum monoreflection on W
s
, denoted , is obtained by contracting the maximum monoreflection on W, and G is epicomplete in W
s
precisely when G is laterally -complete; (iv) the maximum essential reflection on W
s
, denoted , is the contraction of the maximum essential reflection on W.
Received January 22, 1997; accepted in final form June 11, 1998. 相似文献
11.
12.
John W. Snow 《Algebra Universalis》2000,44(1-2):169-185
Suppose is a set of operations on a finite set A. Define PPC() to be the smallest primitive positive clone on A containing . For any finite algebra A, let PPC#(A) be the smallest number n for which PPC(CloA) = PPC(Clo
n
A). S. Burris and R. Willard [2] conjectured that PPC#(A) ≤|A| when CloA is a primitive positive clone and |A| > 2. In this paper, we look at how large PPC#(A) can be when special conditions are placed on the finite algebra A. We show that PPC#(A) ≤|A| holds when the variety generated by A is congruence distributive, Abelian, or decidable. We also show that PPC#(A) ≤|A| + 2 if A generates a congruence permutable variety and every subalgebra of A is the product of a congruence neutral algebra and an Abelian algebra. Furthermore, we give an example in which PPC#(A) ≥|A| - 1)2 so that these results are not vacuous.
Received August 30, 1999; accepted in final form April 4, 2000. 相似文献
13.
Jang Hyun Jo 《代数通讯》2013,41(5):1577-1587
In case G is a finite group, there is a well-known criterion for projective modules: A ? G-module M is projective if and only if it is ? -free and has finite projective dimension. We first investigate whether only finite groups satisfy the above criterion. In the class of groups L H 𝔉, we conclude that this is true. Secondly, we consider the problem when a stably flat Γ-module is projective, where Γ is an arbitrary group. We show that if Γ is an L H 𝔉-group, then every stably flat cofibrant ? Γ-module is projective. 相似文献
14.
Shamil Ishmukhametov 《Archive for Mathematical Logic》1999,38(6):373-386
Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets) and R[d] be the class of less than d r.e. degrees in whichd is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d
R[d] is not empty. We show that the r.e. degree defined by Lachlan for a d.r.e.set
d is just the minimum degree in which D is r.e. Then we study for a given d.r.e. degree d class R[d] and show that there exists a d.r.e.d such that R
d] has a minimum element
0. The most striking result of the paper is the existence of d.r.e. degrees for which R[d] consists of one element. Finally we prove that for some d.r.e. d
R[d] can be the interval [a,b] for some r.e. degrees a,b, a
b
d.
Received: 17 January 1996 相似文献
15.
16.
Boris Širola 《代数通讯》2013,41(9):3267-3279
Suppose G 1 ? G are complex linear simple Lie groups. Let 1 ? be the corresponding pair of Lie algebras. For the Killing-orthogonal of 1 in we have a vector space direct sum = 1⊕ , which generalizes the classical Cartan decomposition on the Lie algebras level. In this article we study the corresponding problem of a ‘generalized global Cartan decomposition’ on the Lie groups level for the pair of groups ( G , G 1) = (SL (4,?),Sp (2,?)); here = (4,?), 1 = (2,?), and = {X ? | X ? = X}, where X? X ? is the symplectic involution. We prove that G = G 1exp ∪ i G 1exp . The key point of the proof is to study in detail the set exp ; and for that purpose we introduce the J-twisted Pfaffian of size 2n defined on the set of all 2n × 2n matrices X satisfying X ? = X, which is here a natural counterpart of the standard Pfaffian. 相似文献
17.
Abstract. Let F be a family of disjoint unit balls in R
3
. We prove that there is a Helly-number n
0
≤ 46 , such that if every n
0
members of F ( | F | ≥ n
0
) have a line transversal, then F has a line transversal. In order to prove this we prove that if the members of F can be ordered in a way such that every 12 members of F are met by a line consistent with the ordering, then F has a line transversal. The proof also uses the recent result on geometric permutations for disjoint unit balls by Katchalski,
Suri, and Zhou. 相似文献
18.
19.
Let A be an abelian group. A group B is A-solvable if the natural map Hom(A, B) ? E(A) A → B is an isomorphism. We study pure subgroups of A-solvable groups for a self-small group A of finite torsion-free rank. Particular attention is given to the case that A is in , the class of self-small mixed groups G with G/tG? ? n for some n < ω. We obtain a new characterization of the elements of , and demonstrate that differs in various ways from the class ? of torsion-free abelian groups of finite rank despite the fact that the quasi-category ? is dual to a full subcategory of ? ?. 相似文献
20.
Yongge Tian 《Annals of the Institute of Statistical Mathematics》2010,62(5):929-941
The weighted least-squares estimator of parametric functions K
β under a general linear regression model { y, X b, s2S }{\{ {\bf y},\,{\bf X \beta}, \sigma^2{\bf \Sigma} \}} is defined to be K[^(b)]{{\bf K}{\hat{\bf {\beta}}}}, where [^(b)]{\hat{{\bf \beta}}} is a vector that minimizes (y − X
β)′V(y − X
β) for a given nonnegative definite weight matrix V. In this paper, we study some algebraic and statistical properties of K[^(b)]{{\bf K}\hat{{\bf \beta}}} and the projection matrix associated with the estimator, such as, their ranks, unbiasedness, uniqueness, as well as equalities
satisfied by the projection matrices. 相似文献