In the present paper

the regular FI algebras have been investigated again based on the idea of classical algebras.Firstly

in regular FI algebras the concept of the MT ideal is proposed by the implication operator

and the connections between MT ideals and congruence relations are discussed;Secondly

in regular FI algebras the prime MT ideals is defined

and the theorem of conditional embedding of regular FI regulars is gained by the prime MT ideals.Thirdly

the characteristic of MT ideals is described with the help of co-triangle-norm on regular FI algebras that is shown by the form of implication operators

and the generating method of MT ideals is given by the theorem of characteristic of MT ideals in regular FI algebras.