期刊论文详细信息
Сибирский математический журнал | |
Construction and Applications of an Additive Basis for the Relatively Free Associative Algebra with the Lie Nilpotency Identity of Degree 5 | |
article | |
S. V. Pchelintsev1  | |
[1] Financial University under the Government of the Russian Federation;Sobolev Institute of Mathematics | |
关键词: Lie nilpotency identity of degree 5; additive basis; central polynomial; kernel polynomial; codimension of a T-ideal; | |
DOI : 10.1134/S0037446620010127 | |
学科分类:数学(综合) | |
来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk | |
【 摘 要 】
We construct an additive basis for the relatively free associative algebra F(5)(K) with the Lie nilpotency identity of degree 5 over an infinite domain K containing $${1 \over 6}$$. We prove that approximately half of the elements in F(5)(K) are central. We also prove that the additive group of F(5)(ℤ) lacks the elements of simple degree ≥ 5. We find an asymptotic estimation of the codimension of T-ideal, which is generated by the commutator [x1,x2,…,x5] of degree 5.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO202106300004598ZK.pdf | 221KB | download |