共查询到20条相似文献,搜索用时 0 毫秒
1.
Stanisław Kasjan 《代数通讯》2013,41(10):3491-3504
Let Λ be an algebra over an algebraically closed field K of infinite transcendence degree over its prime subfield. We prove in particular that if every s-dimensional indecomposable nonprojective Λ-module is Ω-periodic (resp. DTr-periodic) then there exists a common bound for the Ω-periods (resp. DTr-periods) of s-dimensional indecomposable nonprojective Λ-modules. 相似文献
2.
Iain A. Stewart 《Mathematical Logic Quarterly》1994,40(1):132-140
We investigate why similar extensions of first-order logic using operators (that is, generalized quantifiers) corresponding to NP-complete decision problems apparently differ in expressibility: the logics capture either NP or LNP. It had been conjectured that the complexity class captured is NP if and only if the operator is monotone. We show that this conjecture is false. However, we provide evidence supporting a revised conjecture involving finite variations of monotone problems. Mathematics Subject Classification: 68Q15, 03D15, 03C13. 相似文献
3.
4.
Abhijit Dasgupta 《Proceedings of the American Mathematical Society》2001,129(8):2441-2443
Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if is any non-Polish Borel subspace of a Polish space, then , the space of probability Borel measures on with the weak topology, is always true , where is the least ordinal such that is .
5.
Marcin Mostowski 《Mathematical Logic Quarterly》2001,47(4):513-523
We present a method of transferring Tarski's technique of classifying finite order concepts by means of truth‐definitions into finite mode theory. The other considered question is the problem of representability relations on words or natural numbers in finite models. We prove that relations representable in finite models are exactly those which are of degree ≤ o′. Finally, we consider theories of sufficiently large finite models. For a given theory T we define sl(T) as the set of all sentences true in almost all finite models for T. For theories of sufficiently large models our version of Tarski's technique becomes practically the same as the classica one. We investigate also degrees of undecidability for theories of sufficiently large finite models. We prove for some special theory ST that its degree is stronger than 0′ but still not more than Σ02. 相似文献
6.
Roman Wencel 《Mathematical Logic Quarterly》2012,58(6):449-467
Given a group (G, ·), G?Mm, definable in a first‐order structure $\mathcal {M}=(M,\ldots )Given a group (G, ·), G?Mm, definable in a first‐order structure $\mathcal {M}=(M,\ldots )$ equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V?G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in $\mathcal {M}$. These results require a series of preparatory facts concerning dimension functions, some of which might be of independent interest. 相似文献
7.
设O_n是有限链[n]上的保序变换半群.对任意1≤k≤n-1,研究半群O_n(k)={α∈O_n:(x∈[n]x≤k→xα≤k}的秩和幂等元秩,证明了半群O_n(k)的秩为2n-3.进一步,得到了半群O_n(k)(2≤k≤n-1)的幂等元秩为n和半群O_n(1)的幂等元秩为n-1. 相似文献
8.
《代数通讯》2013,41(7):3287-3293
Abstract For an element a of a group G,let S(a) denote the semigroup generated by all conjugates of a in G. We prove that if G is solvable of finite rank and 1 ? S(a) for all 1 ≠ a ∈ G,then ?a G ?/?b G ? is a periodic group for every b ∈ S(a). Conversely if every two generator subgroup of a finitely generated torsion-free solvable group G has this property then G has finite rank,and if every finitely generated subgroup has this property then every partial order on G can be extended to a total order. 相似文献
9.
10.
证明了可选取矩阵X和Hermitian矩阵Z,使得下面的Hermitian型分块矩阵(A XX*Z)取得它的极大秩和极小秩,这里A*=A∈Cm×m是一个已知的复矩阵,X∈Cm×k和Z*=Z∈Ck×k是两个任意的复矩阵. 相似文献
11.
设G是有限秩的剩余有限可解群或是有限秩的剩余有限可解群的有限扩张,α是G的一个索数p阶正则自同构且φ:G→G(g→[g,α])是满射,则G是幂零类不超过h(p)的幂零群,其中h(p)是只与p有关的函数. 相似文献
12.
Ronald Fagin 《Mathematical Logic Quarterly》1997,43(4):431-455
13.
Pete L. Clark 《代数通讯》2018,46(10):4223-4232
The rank rk(R) of a ring R is the supremum of minimal cardinalities of generating sets of I as I ranges over ideals of R. Matsuda and Matson showed that every n∈?+ (the positive integers) occurs as the rank of some ring R. Motivated by the result of Cohen and Gilmer that a ring of finite rank has Krull dimension 0 or 1, we give four different constructions of rings of rank n (for all n∈?+). Two constructions use one-dimensional domains. Our third construction uses Artinian rings (dimension zero), and our last construction uses polynomial rings over local Artinian rings (dimension one, irreducible, not a domain). 相似文献
14.
证明了如何选取矩阵X,Y和Z使得下面的分块矩阵(AXYZ)取得它的极大秩和极小秩,这里A∈C~(m×n)是一个已知矩阵,X∈C~(m×k),Y∈C~(p×n)和Z∈C~(p×k)是三个任意矩阵. 相似文献
15.
John M. Howie Maria Isabel Marques Ribeiro 《Southeast Asian Bulletin of Mathematics》2000,24(2):231-237
This paper is concerned with the application of two possible definitions of rank to certain well-known semigroups.AMS Subject Classification (2000), 20M10 相似文献
16.
17.
A sign pattern matrix is a matrix whose entries are from the set {+,–,0}. The purpose of this paper is to obtain bounds on the minimum rank of any symmetric sign pattern matrix A whose graph is a tree T (possibly with loops). In the special case when A is nonnegative with positive diagonal and the graph of A is star-like, the exact value of the minimum rank of A is obtained. As a result, it is shown that the gap between the symmetric minimal and maximal ranks can be arbitrarily large for a symmetric tree sign pattern A.
Supported by NSF grant No. DMS-00700AMS classification: 05C50, 05C05, 15A48 相似文献
18.
Abhijit Dasgupta 《Proceedings of the American Mathematical Society》2001,129(12):3715-3719
We construct a linear ordering in which every (coanalytic) linear ordering can be order embedded.
19.
It is proved that if G = AB is a soluble group with finite abelian section rank which is factorized by two mutually permutable finite-by-nilpotent subgroups A and B such that A′ and B′ are locally nilpotent, then also the normal closure ? A′, B′ ?G is locally nilpotent and the subgroups A′ and B′ are ascendant in G. 相似文献
20.