References
- Albert , A. A. 1942 . Non-associative algebras. I. Fundamental concepts and isotopy . Ann. Math. , 43 ( 2 ) : 685 – 707 .
- Albert , A. A. 1952 . On nonassociative division algebras . Trans. Amer. Math. Soc. , 72 : 296 – 309 .
- Albert , A. A. 1958 . Finite noncommutative division algebras . Proc. Amer. Math. Soc. , 9 : 928 – 932 .
- Albert , A. A. 1960 . Finite division algebras and finite planes . Proc. Symposia Appl. Math. , 10 : 53 – 70 .
- Albert , A. A. 1961 . Generalized twisted fields . Pacific J. Math. , 11 : 1 – 8 .
- Cordero , M. and Wene , G. P. 1999 . A survey of semifields . Discrete Math. , 208/209 : 125 – 137 . [CROSSREF]
- Dickson , L. E. 1906a . Linear algebras in which division is always uniquely possible . Trans. Amer. Math. Soc. , 7 : 370 – 390 .
- Dickson , L. E. 1906b . On commutative linear algebras in which division is always uniquely possible . Trans. Amer. Math. , 7 : 514 – 522 .
- Dickson , L. E. 1935 . Linear algebras with associativity not assumed . Duke Math. J. , 1 : 113 – 125 . [CROSSREF]
- González , S. , Markov , V. T. , Martínez , C. , Nechaev , A. A. and Rúa , I. F. 2002 . Nonassociative Galois rings . Discrete Math. Appl. , 12 ( 6 ) : 591 – 606 .
- González , S. , Markov , V. T. , Martínez , C. , Nechaev , A. A. and Rúa , I. F. Coordinate sets of generalized Galois rings . Journal of Algebra and its Applications , (to appear)
- Hall , M. Jr. 1959 . The Theory of Groups New York : Macmillan .
- Kaplansky , I. 1975 . Three-dimensional division algebras II . Houston J. Math. , 1 : 63 – 79 .
- Knuth , D. E. 1965a . Finite semifields and projective planes . J. Algebra. , 2 : 182 – 217 .
- Knuth , D. E. 1965b . A class of projective planes . Trans. Amer. Math. Soc. , 115 : 541 – 549 .
- Menichetti , G. 1973 . Algebre tridimensionali su un campo di Galois . Ann. Mat. Pura Appl. , 97 : 293 – 302 .
- Menichetti , G. 1977 . On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field . J. Algebra , 47 : 400 – 410 . [CROSSREF]
- Oehmke , R. H. 1980 . On finite division rings . Proc. Amer. Math. Soc. , 79 : 174 – 176 .
- Schafer , R. D. 1966 . An Introduction to Nonassociative Algebras New York : Academic Press, Inc .
- Walker , R. J. 1962 . Determination of division algebras with 32 elements . Proc. Symposia Appl. Math. , 15 : 83 – 85 .
- Wene , G. P. 1991 . On the multiplicative structure of finite division rings . Aequationes Math. , 41 : 222 – 233 .
- Wene , G. P. 1992 . Semifields of dimension 2n, n ≥ 3, over GF(p m ) that have left primitive elements . Geom. Dedicata , 41 : 1 – 3 . [CROSSREF]
- #Communicated by I. Shestakov.
- aNevertheless, we shall see that this statement is not exactly true.