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Let be an associative algebras over a field of characteristic zero. We prove that the codimensions of are polynomially bounded if and only if any finite dimensional algebra with has an explicit decomposition into suitable subalgebras; we also give a decomposition of the -th cocharacter of into suitable -characters.
We give similar characterizations of finite dimensional algebras with involution whose -codimension sequence is polynomially bounded. In this case we exploit the representation theory of the hyperoctahedral group.
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Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities. 相似文献
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LetAbe a PI-algebra over a fieldF. We study the asymptotic behavior of the sequence of codimensionscn(A) ofA. We show that ifAis finitely generated overFthenInv(A)=limn→∞
always exists and is an integer. We also obtain the following characterization of simple algebras:Ais finite dimensional central simple overFif and only ifInv(A)=dim=A. 相似文献
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EP Sheretov VS Gurov MV Dubkov OV Korneeva 《Rapid communications in mass spectrometry : RCM》1999,13(16):1699-1702
In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd. 相似文献
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By applying the theorem that every positive integer is a sum of four squares, we calculate the exponential growth of the codimensions
for the relatively free algebra satisfying Capelli identities.
Work partially supported by RFFI grants 96-01-00146 and 98-01-01020.
Work partially supported by ISF grant 6629/1.
Work partially supported by RFFI grants 96-01-00146 and 96-15-96050. 相似文献
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The growth of central polynomials for the algebra of n × n matrices in characterstic zero was studied by Regev in [13]. Here we study the growth of central polynomials for any finite-dimensional algebra over a field of characteristic zero. For such an algebra A we prove the existence of two limits called the central exponent and the proper central exponent of A. They give a measure of the exponential growth of the central polynomials and the proper central polynomials of A. We study the range of such limits and we compare them with the PI-exponent of the algebra. 相似文献