On Particular Totally Multiplicatively Prime Algebras

Following Mathiew, Cabrera-Rodriguez and Cabera-Mohammed we define particular totally multiplicatively prime algebra. Using these algebras we improved the result due to Cabera-Mohammed which stated that, if A is a real totally multiplicatively prime algebra, than the central closure of A is a complex totally multiplicatively prime algebra.Also we explain the relation between particular totally multiplicatively prime algebra with prior algebra specifically totally multiplicatively prime algebras ultraprime algebras and totally prime algebras.