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if the answer is yes, tfo entirely SEijifia'Wt fields of research can be united~ 1his paper ;p~1des. conceptually simple geometric construction 1vh1dti',Y1elds an affirmative answer for a broad class of pla.uer. A plane 1t is given by the construction precisely when 1t is a translation p1ar1e with a coordinatizing :right Veblen-Wedderburn system which is(More)
1. Introduction. A ring R is said to be alternative if (xx)y = x(xy), (yx)x=y(xx) for all x, y of R. And R is a division ring if it has a non-zero element and the equations ax = b, ya = b have unique solutions x, y for a ^0; the existence of a unit is not postulated. Let R be an alternative ring without divisors of zero.1 If a, b are nonzero elements of R(More)
L. U. Albers, A. A. Albert, W. R. Allen, D. N. Arden, R. C. F. Bartels, J. H. Bell, Felix Bernstein, R. H. Bing, H. L. Black, C. J. Blackall, W. M. Boothby, D. G. Bourgin, J. W. Bradshaw, Richard Brauer, F. L. Brown, L. M. Browne, R. H. Bruck, W. K. Burroughs, R. E. Carr, E. D. Cashwell, Abraham Charnes, R. V. Churchill, Nathaniel Coburn, C. J. Coe, H. J.(More)
Introduction. If £ is a group with a normal subgroup K one may form the quotient group E/K^M. Conversely, for preassigned groups K, M, there is the extension problem: to determine (in some sense) all groups E with K as normal subgroup such that E/K^M. Much progress has been made on this problem, particularly through the work of Baer [l, 2, 3] and the(More)
1 has conjectured that there exist simple loops of every finite order except order 4. This conjecture is established in §1 by the construction of what we call hyperdbelian loops? In §2 other simple loops are constructed, in particular, loops of order 2/+1 with subloops of order/. The concluding section of the paper is devoted to an investigation of the(More)