Weak-pseudo-R0 Algebras

A positive answer to the open problem of Iorgulescu on extend weak-R₀ algebras and R₀ algebras to the non-commutative forms is given. Some properties, the noncommutative forms of the properties in weak-R₀ algebras and R₀ algebras, are investigated. The simplified axiom systems of weak-pseudo-R₀ algebras and pseudo-R₀ algebras are obtained.