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XXI.—Index Polynomials and Bifurcating Root-Trees*

Published online by Cambridge University Press:  14 February 2012

H. Minc
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Extract

A study is made of faithful representations of the free cyclic (non-associative) groupoid by means of bifurcating root-trees and by means of index polynomials in two indeterminates emphasizing the intimate connection between these representations. The properties of trees and index polynomials are investigated and the concept of lattice of trees is introduced.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 64 , Issue 4 , 1957 , pp. 319 - 341
Copyright
Copyright © Royal Society of Edinburgh 1957

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References

Birkhoff, G., 1935. “On the structure of abstract algebras”, Proc. Camb. Phil. Soc., 31, 433–454.CrossRefGoogle Scholar
Birkhoff, G., 1945. “Universal algebra”, Proc. First Canad. Math. Congr.(Montreal), 310–326.Google Scholar
Birkhoff, G., 1948. Lattice Theory. New York.Google Scholar
Etherington, I. M. H., 1939. “On non-associative combinations”, Proc. Roy. Soc. Edin., 59, 153–162.CrossRefGoogle Scholar
Etherington, I. M. H., 1940, 1945. “Commutative train algebras of ranks 2 and 3”, J. Lond. Math. Soc., 15, 136–149; 20, 238.CrossRefGoogle Scholar
Etherington, I. M. H., 1949. “Non-associative arithmetics”, Proc. Roy. Soc. Edin., A, 62, 442–453.Google Scholar
Etherington, I. M. H. 1951. “Non-commutative train algebras of ranks 2 and 3”, Proc. Lond. Math. Soc., (2), 52, 241–252.Google Scholar
Etherington, I. M. H. 1955. “Theory of indices for non-associative algebra”, Proc. Roy. Soc. Edin., A, 64, 150–160.Google Scholar
Popova, H., 1954. “Logarithmetics of finite quasigroups, I”, Proc. Edin. Math. Soc, (2), 9, 74–81.CrossRefGoogle Scholar