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Derivations in power-associative algebras
Train algebras of degree 2 and exponent 3
1. | Université Polytechnique de Bobo-Dioulasso, 01 BP 1091 Bobo-Dioulasso 01 |
2. | Université de Koudougou, BP 376 Koudougou |
3. | Université de Ouagadougou, 03 BP 7021 Ouagadougou |
4. | Université Montpellier 2, Place Eugène Bataillon, 34095 Montpellier Cedex |
References:
[1] |
A. A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc., 69 (1950), 503-527. |
[2] |
I. Basso, R. Costa, J. Carlos Gutiérrez and H. Guzzo Jr., Cubic algebras of exponent $2$: Basic properties, Int. J. Math. Game Theory and Algebra, 9 (1999), 245-258. |
[3] |
J. Bayara, A. Conseibo and M. Ouattara et F. Zitan, Power-associative algebras that are train algebras, J. Algebra, 324 (2010), 1159-1176.
doi: 10.1016/j.jalgebra.2010.06.012. |
[4] |
H. Guzzo Jr. and P. Vicente, Train algebras of rank $n$ which are Bernstein or power-associative algebras, Nova J. Math. Game Theory Algebra, 6 (1997), 103-112. |
[5] |
H. Guzzo Jr., The Peirce decomposition for commutative train algebras, Comm. Algebra, 22 (1994), 5745-5757.
doi: 10.1080/00927879408825160. |
[6] |
J. Lopez Sanchez and E. Rodriguez S. Maria, On train algebras of rank $4$, Comm. Algebra, 24 (1996), 4439-4445.
doi: 10.1080/00927879608825825. |
[7] |
A. Micali and M. Ouattara, Structure des algèbres de Bernstein, Linear Algebra Appl., 218 (1995), 77-88.
doi: 10.1016/0024-3795(93)00159-W. |
[8] |
M. Ouattara, Sur les T-algèbres de Jordan, Linear Algebra Appl., 144 (1991), 11-21.
doi: 10.1016/0024-3795(91)90056-3. |
[9] |
M. Ouattara, Sur une classe d'algèbres à puissances associatives, Linear Algebra Appl., 235 (1996), 47-62.
doi: 10.1016/0024-3795(94)00113-8. |
[10] |
R. D. Schafer, "An Introduction to Nonassociative Algebras," Academic Press, New York, 1966. |
[11] |
S. Walcher, On Bernstein algebras which are train algebras, Proc. Edinb. Math. Soc. (2), 35 (1992), 159-166.
doi: 10.1017/S0013091500005411. |
[12] |
S. Walcher, Algebras which satisfy a train equation for the first three plenary powers, Arch. Math. (Basel), 56 (1991), 547-551. |
[13] |
A. Wörz-Busekros, "Algebras in Genetics," Lecture Notes in Biomathematics, 36, Springer-Verlag, Berlin-New York, 1980. |
show all references
References:
[1] |
A. A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc., 69 (1950), 503-527. |
[2] |
I. Basso, R. Costa, J. Carlos Gutiérrez and H. Guzzo Jr., Cubic algebras of exponent $2$: Basic properties, Int. J. Math. Game Theory and Algebra, 9 (1999), 245-258. |
[3] |
J. Bayara, A. Conseibo and M. Ouattara et F. Zitan, Power-associative algebras that are train algebras, J. Algebra, 324 (2010), 1159-1176.
doi: 10.1016/j.jalgebra.2010.06.012. |
[4] |
H. Guzzo Jr. and P. Vicente, Train algebras of rank $n$ which are Bernstein or power-associative algebras, Nova J. Math. Game Theory Algebra, 6 (1997), 103-112. |
[5] |
H. Guzzo Jr., The Peirce decomposition for commutative train algebras, Comm. Algebra, 22 (1994), 5745-5757.
doi: 10.1080/00927879408825160. |
[6] |
J. Lopez Sanchez and E. Rodriguez S. Maria, On train algebras of rank $4$, Comm. Algebra, 24 (1996), 4439-4445.
doi: 10.1080/00927879608825825. |
[7] |
A. Micali and M. Ouattara, Structure des algèbres de Bernstein, Linear Algebra Appl., 218 (1995), 77-88.
doi: 10.1016/0024-3795(93)00159-W. |
[8] |
M. Ouattara, Sur les T-algèbres de Jordan, Linear Algebra Appl., 144 (1991), 11-21.
doi: 10.1016/0024-3795(91)90056-3. |
[9] |
M. Ouattara, Sur une classe d'algèbres à puissances associatives, Linear Algebra Appl., 235 (1996), 47-62.
doi: 10.1016/0024-3795(94)00113-8. |
[10] |
R. D. Schafer, "An Introduction to Nonassociative Algebras," Academic Press, New York, 1966. |
[11] |
S. Walcher, On Bernstein algebras which are train algebras, Proc. Edinb. Math. Soc. (2), 35 (1992), 159-166.
doi: 10.1017/S0013091500005411. |
[12] |
S. Walcher, Algebras which satisfy a train equation for the first three plenary powers, Arch. Math. (Basel), 56 (1991), 547-551. |
[13] |
A. Wörz-Busekros, "Algebras in Genetics," Lecture Notes in Biomathematics, 36, Springer-Verlag, Berlin-New York, 1980. |
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