Proper central and core polynomials of relatively free associative algebras with identity of Lie nilpotency of degrees 5 and 6
- Moscow State Pedagogical University (Russian Federation)
We study the centre of a relatively free associative algebra F{sup (n)} with the identity [x{sub 1},…,x{sub n}]=0 of Lie nilpotency of degree n=5,6 over a field of characteristic 0. It is proved that the core Z{sup ∗}(F{sup (5)}) of the algebra F{sup (5)} (the sum of all ideals of F{sup (5)} contained in its centre) is generated as a T-ideal by the weak Hall polynomial [[x,y]{sup 2},y]. It is also proved that every proper central polynomial of F{sup (5)} is contained in the sum of Z{sup ∗}(F{sup (5)}) and the T-space generated by [[x,y]{sup 2},z] and the commutator [x{sub 1},…,x{sub 4}] of degree 4. This implies that the centre of F{sup (5)} is contained in the T-ideal generated by the commutator of degree 4. Similar results are obtained for F{sup (6)}; in particular, it is proved that the core Z{sup ∗}(F{sup (6)}) is generated as a T-ideal by the commutator of degree 5. Bibliography: 15 titles. (paper)
- OSTI ID:
- 22876127
- Journal Information:
- Sbornik. Mathematics, Vol. 207, Issue 12; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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