On the invariance of subspaces in some baric algebras
DOI:
https://doi.org/10.4067/S0716-09172003000100006Abstract
In this article, we look for invariance in commutative baric algebras (A, ?) satisfying (x 2 ) 2 = ?(x)x 3 and in algebras satisfying (x 2 ) 2 = ?(x 3 )x, using subspaces of kernel of ? that can be obtained by polynomial expressions of subspaces Ue e Ve of Peirce decomposition A = Ke ? Ue ? Ve of A, where e is an idempotent element. Such subspaces are called p -subspaces. Basically, we prove that for these algebras, the p -subspaces have invariant dimension, besides that, we find out necessary and sufficient conditions for the invariance of the p-subspaces.
References
[2] R. Andrade and A. Labra. On a class of Baric Algebras. Linear Algebra and its Applications, 245, pp. 49–53, (1996)
[3] R. Costa and J. Pican¸co. Invariance of dimension of p-subspaces in B ernstein algebras. Communications in Algebra, 27 (8), pp. 4039-4055 (1999).
[4] I. M. H. Etherington. Commutative train algebras of ranks 2 and 3. J. London Math. Soc. 15, pp. 136-149, (1940)
[5] C. Mallol and R. Varro. A propos des algèbres vérifiant x [3] = ?(x) 3x. Linear Algebra and its Applications, 225, pp. 187–194, (1995).
[6] S. Walcher. Algebras which satisfy a train equation for the first three plenary powers. Arch. Math. 56, pp. 547–551, (1991).
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.