Geodesic
On the Lower Central Factors of a Free Associative Ring
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 434-438

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a free associative ring with identity freely generated by r1, r2,. .. , rk. In analogy to group theory the lower central series for R is defined inductively Byγo = R and γn = [γn-1, R],where γn is the ideal generated by the indicated ring commutators. Using P. Hall's collection process [2; 1, Chapter 11] γn/γn+1 will be shown to be free as a Z-module and as an R/R''-module for each non-negative integer n. In each case a basis will be exhibited. Definition 1. Commutators of order zero are the free generators of R. A commutator, c, of order n (denoted by o(c) = n) is of the form [x, y], where x and y are commutators and o(x) + o(y) = n — 1. 
Tyler, Robert. On the Lower Central Factors of a Free Associative Ring. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 434-438. doi: 10.4153/CJM-1975-051-6
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[1] 1. Hall, M., Jr., The theory of groups (The Macmillan Company, New York, 1959). Google Scholar

[2] 2. Hall, P., A contribution to the theory of groups of prime power order, Proc. London Math. Soc. 36 (1933), 29–95. Google Scholar

[3] 3. Jennings, S., Central chains of ideals in an associative ring, Duke Math. J. 9 (1942), 341–355. Google Scholar

[4] 4. Magnus, W., Karrass, A., and Solitar, D., Combinatorial group theory (Interscience, New York, 1966). Google Scholar

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