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S. A. Gurchenkov 《Algebra and Logic》1995,34(4):219-222
An Engel l-group generating a proper normal-valued l-variety is shown to be o-approximable. It is also established that for every proper normal-valued l-varietyF, the class (F) of Engel l-groups from F is a torsion class.Translated fromAlgebra i Logika, Vol. 34, No. 4, pp. 398–404, July-August, 1995. 相似文献
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Arye Juhász 《Israel Journal of Mathematics》1990,69(1):1-24
In this series of papers we study Engel groups through their presentation, using Small Cancellation Theory. In the present
paper we describe the consequences of a single Engel relator. 相似文献
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We study m-dimensional real submanifolds M with (m − 1)-dimensional maximal holomorphic tangent subspace in complex projective space. On these manifolds there exists an almost
contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX, Y) − h(X, FY) = g(FX, Y)η, η ∈ T
⊥(M), on the almost contact structure F and on the second fundamental form h of these submanifolds and we characterize certain model spaces in complex projective space. 相似文献
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Let F denote a free group. An n-Engel word of F is an iterated commutator of the form [A, nB], where (A,B) is a pair of elements of F, which we here assume to generate a non-cyclic subgroup of F. This is the second of a series of three papers that examine some of the properties of a group defined by a suitable set
of relators of the form [A
i
, nB
i
], i = 1, 2, ...,m (where n is fixed). In the present paper, the techniques of [1] are generalised in a way that permits the application of
the conclusions of [1] concerning the nature of the consequences of a single Engel relator to the case of a finite number
of n-Engel relators, subject only to some mild hypotheses on the lengths of the relators and the value of n. 相似文献
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Thomas Vogel 《Comptes Rendus Mathematique》2005,340(1):43-48
Every 4-manifold with trivial tangent bundle admits an Engel structure. To cite this article: T. Vogel, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Sandro Mattarei 《Linear and Multilinear Algebra》2013,61(4):441-449
In a recent study of Engel Lie rings, Serena Cicalò and Willem de Graaf have given a practical set of conditions for an additively finitely generated Lie ring L to satisfy an Engel condition. We present a simpler and more direct proof of this fact. Our main result generalizes this in the language of tensor algebra, and describes a relatively small generating set for the module generated by all n-th tensor powers of elements of a finitely generated ?-module M, in terms of a generating set for M. 相似文献
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Yangkok Kim 《代数通讯》2013,41(8):3023-3027
It is known that an orderable n-Engel group is nilpotent. We show that an orderable group that is an extension of an n-Engel group by an n-Engel group is nilpotent-by-nilpotent. However, a finitely generated orderable poly n-Engel group need not be solvable in general. 相似文献
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Enrico Picelli 《Archiv der Mathematik》2006,87(4):289-294
The relation between the Engel structure of a semilocal ring and that of its multiplicative group is investigated. Suppose
that every local ring whose multiplicative group satisfies an m-Engel condition for some positive integer m is an f (m)-Engel ring for some function f . It is proved that under this condition a corresponding statement holds for every semilocal ring which is generated by its
multiplicative group.
Received: 20 September 2005 相似文献
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Charles Lanski 《代数通讯》2013,41(1):139-152
It is known that for a nonzero derivation d of a prime ring R, if a nonzero ideal I of R satisfies the Engel-type identity [[…[[d(x k 0 ), x k 1 ], x k 2 ],…], x k n ], then R is commutative. Here we extend this result to a skew derivation of R for a Lie ideal I, which has an immediate corollary that replaces d by an automorphism of R. A related result in two variables is obtained for d a (θ, ?)-derivation. 相似文献
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Jiro Adachi 《Mathematische Zeitschrift》2013,273(3-4):711-733
The conditions to determine germs of Engel structures relative to arbitrary subsets are studied. We show that germs of Engel structures at a point relative to an arbitrary subset are determined by the algebraic restrictions of the Engel structures themselves to the subset, and the projected algebraic restrictions of the derived even-contact structures to the subset. When the subset is a smooth submanifold, algebraic restriction is equivalent to geometric restriction. Even when the subset is a smooth submanifold, we need a new stricter notion, projected algebraic restriction. 相似文献
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We prove that, if A is left-nil Novikov algebra, then A 2 is nilpotent. 相似文献
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Mathematical Notes - 相似文献
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Hansjörg Geiges 《Mathematische Annalen》2008,342(2):291-296
A simple proof is given of the following result first observed by Adachi: embedded circles tangent to the standard Engel structure
on are classified, up to isotopy via such embeddings, by their rotation number. 相似文献
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