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Abelian Steiner Triple Systems

Published online by Cambridge University Press:  20 November 2018

Peter Tannenbaum
Peter Tannenbaum*
Affiliation:
University of California, Santa Barbara, California
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A neofield of order v, Nv( + , •), is an algebraic system of v elements including 0 and 1,0 ≠ 1, with two binary operations + and • such that (Nv, + ) is a loop with identity element 0; (Nv*, •) is a group with identity element 1 (where Nv* = Nv\﹛0﹜) and every element of Nv is both right and left distributive (i.e., (y + z)x = yx + zx and x(y + z) = xy + xz for all y, z∈ Nv).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1251 - 1268
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Doner, J. R., CIP neofields and combinatorial designs, Ph.D. dissertation, University of Michigan, 1972.Google Scholar
2. Johnsen, E. C. and Storer, T. F., Combinatorial structures in l∞ps, II; Commutative inverse property cyclic neofields of prime-power order, Pacific J. Math. 52 (1974), 115–127.Google Scholar
3. Johnsen, E. C. and Storer, T. F., Combinatorial structures in l∞ps, IV; Steiner triple systems in Neofields, Math. Z. 138 (1974), 1–14.Google Scholar