Elementary equivalence of linear groups over rings with a finite number of central idempotents and over Boolean rings

In the present paper, we start with a criterion of elementary equivalence of linear groups over rings with just a finite number of central idempotents. Then we study elementary equivalence of linear groups over Boolean algebras. We prove that two linear groups over Boolean algebras are elementarily equivalent if and only if their dimensions coincide and these Boolean algebras are elementarily equivalent.