共查询到20条相似文献,搜索用时 15 毫秒
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A. Salwa 《Archiv der Mathematik》2002,78(5):350-357
Decompositions of simple artinian rings as additive sums of nilpotent subrings are considered. In particular, necessary and sufficent conditions for minimal decompositions are found in terms of the underlying division ring. This is used to prove that any algebra with 1 can be unitarily embedded into a simple algebra with 1 which is a sum of four subalgebras with zero multiplication and also into a simple algebra which is a sum of three nilpotent subalgebras of degree 3. Since our proof is constructive and is based on simple artinian rings, the latter result can be viewed as an extension and a strengthened version of Bokut's theorem, [2]. 相似文献
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Czechoslovak Mathematical Journal - Let k be a field of characteristic zero and B a k-domain. Let R be a retract of B being the kernel of a locally nilpotent derivation of B. We show that if B = R... 相似文献
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We study the structure of rings that are sums of two subrings one of which is nil and the other reduced. Our main results concern the problem whether in this situation the nil subring must be an ideal.Received: 13 July 2001 相似文献
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In the article we show that the sum of two PI-rings is again a PI-ring.Translated fromAlgebra i Logika, Vol. 34, No. 1, pp. 3–11, January–February, 1995.Supported by the Russian Foundation for Fundamental Research, grant No. 93-011-01544. 相似文献
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B. Felzenszwalb 《Israel Journal of Mathematics》1976,23(2):156-164
LetR be a ring with a subringA such that a power of every element ofR lies inA. The following results are proved: IfR has no nonzero nil right ideals, neither doesA; if moreoverR is prime,A is also prime. IfR is semiprime Goldie, so isA. IfA has no nonzero nilpotent elements, then the nilpotent elements ofR form an ideal. Finally ifR has no nil right ideals andA is Goldie, thenR is Goldie.
This work was supported by the National Research Council of Brazil (CNPq) at the University of Chicago.
The author wishes to express his gratitude to Professor I. N. Herstein for his advise and encouragement. 相似文献
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Florian Luca Pantelimon Stanica 《Proceedings of the American Mathematical Society》2005,133(7):1887-1890
In this paper, we construct an infinite arithmetic progression of positive integers such that if , then the th Fibonacci number is not a sum of two prime powers.
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B. A. F. Wehrfritz 《Journal of Pure and Applied Algebra》1989,60(3):289-312
Say a division ring D is special if for every finite subset X of D there is a homomorphism of the subring of D generated by X into a division ring of finite Schur index a power of its positive characteristic. (D is not assumed to have positive characteristic.) We make a detailed study of nilpotent and locally nilpotent matrix groups over special division rings.
This has been done previously for a number of ‘special’ division rings arising from group algebras and Lie algebras, particularly by A.I. Lichtman. The present paper therefore presents single proofs of all these results. It also covers many division rings not considered before and produces some new results for those that have been considered before.
In view of the definition of ‘special’ it is not surprising that the proofs depend on a detailed analysis of the finite-dimensional case. 相似文献
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C Hooley 《Journal of Number Theory》1973,5(3):215-217
It is proved that for given unequal positive numbers h, k there exist infinitely many natural numbers n for which n, n + h, n + k are all sums of two squares. 相似文献
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