In a recent study of Engel Lie rings, Serena Cicaló 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 ℤ-module M, in terms of a generating set for M.
Mattarei, S. (2011). Engel conditions and symmetric tensors. LINEAR & MULTILINEAR ALGEBRA, 59(4), 441-449 [10.1080/03081081003621295].
Engel conditions and symmetric tensors
Mattarei, S
2011
Abstract
In a recent study of Engel Lie rings, Serena Cicaló 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 ℤ-module M, in terms of a generating set for M.
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