共查询到20条相似文献,搜索用时 15 毫秒
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Jin Bai Kim 《Linear algebra and its applications》1974,8(4):313-325
Let M and N be two subspaces of a finite dimensional vector space V over a finite field F. We can count the number of all idempotent linear transformations T of V such that R(T) ?M and N?N(T), where R(T) and N(T) denote the range space and the null space of T, respectively. 相似文献
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Janusz Konieczny 《Central European Journal of Mathematics》2011,9(1):23-35
For an infinite set X, denote by Γ(X) the semigroup of all injective mappings from X to X under function composition. For α ∈ Γ(X), let C(α) = {β ∈ g/g(X): αβ = βα} be the centralizer of α in Γ(X). The aim of this paper is to determine those elements of Γ(X) whose centralizers have simple structure. We find α ∈ (X) such that various Green's relations in C(α) coincide, characterize α ∈ Γ(X) such that the $
\mathcal{J}
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\mathcal{J}
-classes of C(α) form a chain, and describe Green's relations in C(α) for α with so-called finite ray-cycle decomposition. If α is a permutation, we also find the structure of C(α) in terms of direct and wreath products of familiar semigroups. 相似文献
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Caterina Stoppato 《Annals of Global Analysis and Geometry》2011,39(4):387-401
Quaternionic Moebius transformations have been investigated for more than 100 years and their properties have been characterized in detail. In recent years G. Gentili and D. C. Struppa introduced a new notion of regular function of a quaternionic variable, which is developing into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the non-commutative setting introduces new phenomena. Unfortunately, the (classical) quaternionic Moebius transformations are not regular. However, in this paper we are able to construct a different class of Moebius-type transformations that are indeed regular. This construction requires several steps: we first find an analog to the Casorati-Weierstrass theorem and use it to prove that the group \({Aut(\mathbb{H})}\) of biregular functions on \({\mathbb{H}}\) coincides with the group of regular affine transformations. We then show that each regular injective function from \({\widehat{\mathbb{H}} = \mathbb{H}\cup \{\infty\}}\) to itself belongs to a special class of transformations, called regular fractional transformations. Among these, we focus on the ones which map the unit ball \({\mathbb{B} = \{q \in \mathbb{H} : |q| < 1 \}}\) onto itself, called regular Moebius transformations. We study their basic properties and we are able to characterize them as the only regular bijections from \({\mathbb{B}}\) to itself. 相似文献
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Miriam Cohen 《Israel Journal of Mathematics》1975,20(1):37-45
LetG be a finite group of automorphisms acting on a ringR, andR G={fixed points ofG}. We show that under certain conditions onR andG, whenR Gis semiprime Goldie then so isR. In particular, ifa∈R is invertible anda n∈Z(R), thenR G,withG generated by the inner automorphism determined bya, is the centralizer ofa—C R(a). The above result withR Greplaced byC R(a) is shown without the assumption thata is invertible. 相似文献
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Félix Cabello Sánchez 《Mathematische Annalen》2014,358(3-4):779-798
It is shown that every nonlinear centralizer from $L_p$ to $L_q$ is trivial unless $q=p$ . This means that if $q\ne p$ , the only exact sequence of quasi-Banach $L_\infty $ -modules and homomorphisms $0\rightarrow L_q\rightarrow Z\rightarrow L_p\rightarrow 0$ is the trivial one where $Z=L_q\oplus L_p$ . From this it follows that the space of centralizers on $L_p$ is essentially independent on $p\in (0,\infty )$ , which confirms a conjecture by Kalton. 相似文献
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Let ${\mathcal{L}}$ be a subspace lattice on a complex Banach space X and δ be a linear mapping from ${alg\mathcal{L}}$ into B(X) such that for every ${A \in alg\mathcal{L}, 2\delta(A^2)=\delta(A)A + A\delta(A)}$ or ${\delta(A^3) = A\delta(A)A}$ . We show that if one of the following holds (1) ${\vee\{L : L \in \mathcal{J}(\mathcal{L})\}=X}$ , (2) ${\wedge\{L_-: L \in \mathcal{J}(\mathcal{L})\}=(0)}$ and X is reflexive, then δ is a centralizer. We also show that if ${\mathcal{L}}$ is a CSL and δ is a linear mapping from ${alg\mathcal{L}}$ into itself, then δ is a centralizer. 相似文献
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S. T. L. Choy 《Acta Mathematica Hungarica》1987,49(1-2):151-155
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C.S. Ballantine 《Linear algebra and its applications》1978,19(1):81-86
For some years it has been known that every singular square matrix over an arbitrary field F is a product of idempotent matrices over F. This paper quantifies that result to some extent. Main result: for every field F and every pair (n,k) of positive integers, an n×n matrix S over F is a product of k idempotent matrices over F iff rank(I ? S)?k· nullity S. The proof of the “if” part involves only elementary matrix operations and may thus be regarded as constructive. Corollary: (for every field F and every positive integer n) each singular n×n matrix over F is a product of n idempotent matrices over F, and there is a singular n×n matrix over F which is not a product of n ? 1 idempotent matrices. 相似文献
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A. N. Abyzov 《Russian Mathematics (Iz VUZ)》2011,55(8):1-6
For arbitrary modules A and B we introduce and study the notion of a fully idempotent Hom (A, B). As a corollary we obtain some well-known properties of fully idempotent rings and modules. 相似文献