共查询到20条相似文献,搜索用时 562 毫秒
1.
《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
2.
《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
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 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
5.
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
6.
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
7.
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
8.
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.
Xian Zhang 《Linear and Multilinear Algebra》2013,61(5):349-358
Suppose F is a field of characteristic not 2. Let Mn F and Sn F be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from Sn F to Sn F (respectively, Mn F) preserving Moore–Penrose inverses of matrices are characterized. We first characterize all additive Moore–Penrose inverse preserving maps from Sn F to Mn F, and thereby, all additive Moore–Penrose inverse preserving maps from Sn F to itself are characterized by restricting the range of these additive maps into the symmetric matrix space. 相似文献
11.
Garrett Birkhoff conjectured in 1942 that when A, B, P are finite posets satisfying A
PB
P, then AB. We show that this is true. Further, we introduce an operation C(A
B), related to Garrett Birkhoff's exponentiation, and determine the structure of the algebra of isomorphism types of finite posets under the operations induced by A+B, A×B, and C(A
B). Every finite +-indecomposable and ×-indecomposable poset A of more than one element is expressible for unique (up to isomorphism) E and P as AC(E
P) where P is connected and E is indecomposable for all three operations. 相似文献
12.
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
13.
Ralph McKenzie 《Order》1999,16(4):313-333
Garrett Birkhoff conjectured in 1942 that when A, B, P are finite posets satisfying A
P
B
P
, then A B. We show that this is true in case P is dismantlable to each of its points, or P is connected and each of A and B is dismantlable to each of its covering pairs. 相似文献
14.
Jörg Stephan 《Order》1993,10(2):133-142
Some relations between the classB of lattices of breadth at most two and its subclassD of dismantlable lattices, as well as the lattice varietiesV (B) andV (D) generated byV (D) andV (D), respectively, are studied in this paper. For finite join-semidistributive lattices, the two concepts of dismantlability and breadth at most two coincide. There are infinitely many lattice varieties between the varietiesV (D) andV (B), none of them is finitely based. 相似文献
15.
Let {ξ
j
; j ∈ ℤ+
d
be a centered stationary Gaussian random field, where ℤ+
d
is the d-dimensional lattice of all points in d-dimensional Euclidean space ℝd, having nonnegative integer coordinates. For each j = (j
1
, ..., jd) in ℤ+
d
, we denote |j| = j
1
... j
d
and for m, n ∈ ℤ+
d
, define S(m, n] = Σ
m<j≤n
ζ
j
, σ2(|n−m|) = ES
2
(m, n], S
n
= S(0, n] and S
0
= 0. Assume that σ(|n|) can be extended to a continuous function σ(t) of t > 0, which is nondecreasing and regularly varying with exponent α at b ≥ 0 for some 0 < α < 1. Under some additional conditions, we study limsup results for increments of partial sum processes and prove as well the law of the iterated logarithm for such partial sum processes.
Research supported by NSERC Canada grants at Carleton University, Ottawa 相似文献
16.
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
17.
C. Luppi 《Archive for Mathematical Logic》2002,41(5):443-454
Let L be one of the intuitionistic modal logics considered in [4]. As in the classical modal case (see [7]), we define two different
forms of the Beth property for L, which are denoted by B
1
and B
2
; in this paper we study the relation among B
1
,B
2
and the interpolation properties C
1
and C
2
, introduced in [4]. It turns out that C
1
implies B
1
, but contrary to the boolean case, is not equivalent to B
1
. It is shown that B
2
and C
2
are independent, and moreover it comes out that, in contrast to classical case, there exists an extension of the intuitionistic
modal logic of S
4
-type, that has not the property B
2
. Finally we give two algebraic properties, that characterize respectively B
1
and B
2
.
Received: 27 September 1999 / Published online: 31 May 2002 相似文献
18.
Abram Kagan Paul J. Smith 《International Journal of Mathematical Education in Science & Technology》2013,44(1):91-96
Using appropriately parameterized families of multivariate normal distributions and basic properties of the Fisher information matrix for normal random vectors, we provide statistical proofs of the monotonicity of the matrix function A -1 in the class of positive definite Hermitian matrices. Similarly, we prove that A 11 < A -111, where A 11 is the principal submatrix of A and A 11 is the corresponding submatrix of A -1. These results in turn lead to statistical proofs that the the matrix function A -1 is convex in the class of positive definite Hermitian matrices and that A 2 is convex in the class of all Hermitian matrices. (These results are based on the Loewner ordering of Hermitian matrices, under which A < B if A - B is non-negative definite.) The proofs demonstrate that the Fisher information matrix, a fundamental concept of statistics, deserves attention from a purely mathematical point of view. 相似文献
19.
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