A Block Triangular Matrix Algebra To Maintain The Rank Of A Linear Surjection

"Linear preserver problems" is a both old and young project. It has more than one hundred years old. By now, it is quite active and more new researches emerge in this area. In this paper we first give the definition of a type of block upper triangular matrix algebras and then characterize linear surjective maps that preserve rank one from one block upper triangular matrix algebra of this type to another. We undertake a further investigation of rank one preserver problems studied by Jeremy, Bell, A.R.Sourour, Marcus and Moyls etc.