Home > Mathematics, Statistics > Vol 10 No 1 June 2022 Abstract 5
On Pre-Hilbert Algebras Containing a nonzero Central Idempotent ?? such that ???? = ?? and ???? = ?? ??
Noureddine Motya, Hakima Mouanis, Abdelhadi Moutassim

Abstract
Let ?? be a real pre-Hilbert algebra without divisors of zero, we prove that if ?? has dimension two and satisfying ??2 = ?? 2 , for all ?? ? ?? , Then ?? is isomorphic to a new classes of two dimensional pre-Hilbert algebras. We also characterize the pre-Hilbert algebraic algebras without divisors of zero and containing a nonzero central idempotent ?? such that ???? = ?? and ??2 = ?? 2, to be flexible algebras. Furthermore, we prove that if ?? contains a nonzero central idempotent ?? such that ???? = ?? and ??2 = ?? 2 for all ?? in ??, then the following statements are equivalent: 1. ?? is power commutative 2. ?? is third power associative 3. ?? is algebraic of degree two.

Full Text: PDF     DOI: 10.15640/arms.v10n1a5