ON THE INVARIANCE OF SUBSPACES IN SOME BARIC ALGEBRAS

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.