On the invariance of subspaces in some baric algebras
Author
Basso, I.
Costa, R.
Picanco, J.
Abstract
In this article, we look for invariance in commutative baric algebras (A, ω) satisfying (x 2 ) 2 = ω(x)x 3 and in algebras satisfying (x 2 ) 2 = ω(x 3 )x, using subspaces of kernel of ω 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.