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31.
The crystal structure of quasi-one-dimensional compound Ni[S2CPyrd]2 (Pyrd=pyrrolidine) has been determined by X-ray diffraction technique. It crystallizes in the monoclinic system, space group P21/c, with lattice parameters a=0.631 6(1) nm, b=0.746 5(2) nm, c=1.576 5(4) nm, β=106.08(3)°, and Z=2. The nickel atom had a square-planar geometry. The most prominent feature in the crystal structure is that the bis(pyrrolidinedithiocarbamato) nickel(Ⅱ) forms a well-separated stacking column along the a-axis through supramolecular interaction, and they are uniformly spaced to give a helical one-dimensional chain structure. CCDC: 220648. 相似文献
32.
S. M. Bhatwadekar Amartya K. Dutta 《Transactions of the American Mathematical Society》1997,349(8):3303-3319
In this paper we study the kernel of a non-zero locally nilpotent -derivation of the polynomial ring over a noetherian integral domain containing a field of characteristic zero. We show that if is normal then the kernel has a graded -algebra structure isomorphic to the symbolic Rees algebra of an unmixed ideal of height one in , and, conversely, the symbolic Rees algebra of any unmixed height one ideal in can be embedded in as the kernel of a locally nilpotent -derivation of . We also give a necessary and sufficient criterion for the kernel to be a polynomial ring in general.
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34.
Let R be a noncommutative prime ring and I a nonzero left ideal of R. Let g be a generalized derivation of R such that [g(r k ), r k ] n = 0 for all r ∈ I, where k, n are fixed positive integers. Then there exists c ∈ U, the left Utumi quotient ring of R, such that g(x) = xc and I(c ? α) = 0 for a suitable α ∈ C. In particular we have that g(x) = α x, for all x ∈ I. 相似文献
35.
A ring R is simple under a set D of derivations if no nontrivial ideal of R is preserved by all derivations in D. Continuing previous joint work with C. J. Maxson, the author provides a computational test for the simplicity of k[x 1,…,x n ]/〈 x 1 p ,…, x n p 〉 (k a field of characteristic p > 0) under a set of commuting k-derivations. Specific rings are then examined for sets of commuting derivations, especially those under which the ring is simple. The possible sizes and minimality of such sets are also determined in particular cases. 相似文献
36.
37.
Concerning the stability problem of functional equations, we introduce a general (m, n)-Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general (m, n)-Cauchy-Jensen additive mappings in C*-algebras, which generalize the results obtained for Cauchy-Jensen type additive mappings. 相似文献
38.
Let F be a field of characteristic 0, Mn(F) the full matrix algebra over F, t the subalgebra of Mn(F) consisting of all upper triangular matrices. Any subalgebra of Mn(F) containing t is called a parabolic subalgebra of Mn(F). Let P be a parabolic subalgebra of Mn(F). A map φ on P is said to satisfy derivability if φ(x·y) = φ(x)·y+x·φ(y) for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn(F) is an inner derivation. 相似文献
39.
陈正新 《数学物理学报(B辑英文版)》2014,(3):814-828
Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) = 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation. 相似文献
40.
Andreas Maurischat 《代数通讯》2019,47(7):2617-2633
The multidimensional chain rule formula for analytic functions and its generalization to higher derivatives perfectly work in the algebraic setting in characteristic zero. In positive characteristic one runs into problems due to denominators in these formulas. In this article we show a direct analog of these formulas using higher derivations which are defined in any characteristic. We also use these formulas to show how higher derivations to different coordinate systems are related to each other. Finally, we apply this to polynomial automorphisms in arbitrary characteristic and obtain a formula for the inverse of such a polynomial automorphism. 相似文献