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Can eve.ry (non-Desarguest.. an) projee.,tJVe p~' ~ imbedded (in some natural, g~anet.ric ff.hion) in af1J8sarguesian) projective space? The Ite,titn is ne...WI~.ut .. ,trnp .. · ortant, for, 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(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)
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)
Introduction. A. A. Albert [l, I I ] 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(More)
S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation a t meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number(More)
Introduction. In this paper we shall be concerned with the structure of the rational representation of certain sets of matrices, to which we give the name generalized Fischer sets. If K is any field, <j> any fixed automorphism of K, and A any matrix with elements in K, we use the notation A* for the 0-automorph of A ; that is, the matrix obtained from A by(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)
It should be noted that the definition (introduced in [l]) of a normal endomorphism of a loop G is radically different from the usual definition for groups. Nevertheless (as shown in [2]) the two definitions are equivalent when G is a group. In particular, the present theorem generalizes one of Heerema [3]. We may add that in [2], by assuming that the loop(More)