The November Meeting in St, Louis
نویسندگان
چکیده
s of all papers presented at the meeting are given below. Papers read by title are indicated by the letter t" Paper number 48 was presented by Professor Chatland, number 54 by Mr. Block, number 58 by Professor Ulrich, number 72 by Mr. Kelly, and number 82 by Dr. Moise. ALGEBRA AND THEORY OF NUMBERS 47/. A. A. Albert: Power-associative rings. I I . A power-associative algebra A over a field F is trace-admissible when there is a function t(x, y) on A, A to .Fsuch that t(x, y) =t(y, x), t(xy, z) —t(x, yz), t(x, y) =0 if xy is nilpotent, t(e, e) 7*0 if e is idempotent. When the radical is defined to be the maximal nilideal a trace-admissible algebra has the usual structure properties. An algebra A is called a standard algebra if the identities z(xy)+y(zx)-\"(zy)x=*z(yx) +(zx)y+(yz)xt w[x(yz) ] + [ (wy)x]z+ [(wz)x]y = (tew) (yz)+(wy) (xz) + (wz) (xy) are satisfied. All associative and Jordan algebras are standard. All standard nilagebras are solvable and all solvable standard algebras strongly nilpotent. If the field is nonmodular standard algebras are trace-admissible and the radical of A is the radical of the Jordan algebra A>. For every algebra A there is an attached algebra A (X) defined by the product X'y=*\xy-{-(l —\)yx for X in F. Then ATM =*A(l/2). The author calls A over F quasiassociative if there exists an extension K such that AR^BÇK) for B associative and X in K. Then either A is associative or X—X is in F. He calls A /-simple if -4(1/2) is a simple Jordan algebra, and shows that all flexible /-simple algebras are either the exceptional Jordan algebra or quasiassociative. In particular, every simple standard algebra is either associative or a Jordan algebra. (Received October 13, 1947.) 48. Harold Chatland and H. B. Mann: On extensions of domains of
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