Group of automorphisms of one class of formal matrix algebras

The structure of the automorphism group of a formal matrix algebra over a commutative ring has been found under certain conditions. The automorphism group of such algebra is a semidirect product of several subgroups consisting of automorphisms with a known structure. This is achieved due to the fact that the formal matrix algebra is represented as a splitting extension of a certain nilpotent ideal by means of the product of ordinary matrix rings.