共查询到10条相似文献,搜索用时 62 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.
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
3.
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
4.
《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
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.
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
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.
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
10.
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