On the invariance of subspaces in some baric algebras
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.
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