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Independence and nilpotency in algebras. (Russian)
Authors: Chekanu G. P., Cojuhari Elena
Abstract
In the work the following theorem about the independence is proved: if the word $w$ is maximal among all nonzero products of length not exceeding $n$ and all the ends of $w$ are nilpotent, then all the beginning a linear-independent. Some applications of this theorem are pointed out. Particularly, the truth of I.Shestakov's conjecture is confirmed, another proof of Wedderburn theorem about the nilpotency of a finitedimensional algebra with a nil bases is given. This proof does not use classic structure results.Institutul de Matematica Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău MD-2028, Moldova
str. Academiei 5, Chişinău MD-2028, Moldova
Contents
- An algorithm for forming the Poincare cycle. (Russian)
- A property of the rings of endomorphisms. (Romanian)
- On solution of problems of integer programming. (Russian)
- Rates of queue length convergence for priority queues with orientation. (English)
- On the commutator of two operators in sandwiches. (Russian)
- Idempotents and the radical with respect to a right ideal. (Russian)
- Independence and nilpotency in algebras. (Russian)
- On isomorphisms of free topological groups, rings and modules generated by topological spaces. (Russian)
- Modeling of self-dual Boolean functions commuting with 1 in a 3-valued extension of provability-intuitionistic logic. (Russian)
- $L\sb 2$ estimates for singularly perturbed onedimensional hyperbolic equations of high order. (English)
- On the group of motions of the four-dimensional hyperbolic space of a $120$-hedron. (Russian)
