Automorphism Groups of Formal Matrix Rings

Automorphisms of Formal Matrix Rings

“…In the given paper, we significantly amplify some results of [20] and give many new results on automorphisms of formal matrix rings. We also study automorphisms of ordinary matrix rings (in particular, triangular matrix rings).…”

“…Automorphisms and isomorphisms of various matrix rings are studied in many papers; for example, see [1], [3], [4], [10], [11], [12], [13], [17], [18], [20], [22], [26], [27]. Some other mappings of matrix rings were also studied; in particular, commuting and centralizing mappings were studied (for example, see [24]).…”

“…Some other mappings of matrix rings were also studied; in particular, commuting and centralizing mappings were studied (for example, see [24]). The author's work [20] is devoted to automorphisms and homomorphsms of formal matrix algebras. First, the authors consider automorphisms of the algebra S = L ⊕ M, where L is some subalgebra and M is a nilpotent ideal.…”

“…First, the authors consider automorphisms of the algebra S = L ⊕ M, where L is some subalgebra and M is a nilpotent ideal. In such a case, one says that S is a splitting extension of the ideal M by the subalgebra L. In [20], results on the group Aut S are applied to formal matrix algebras. At the same time, some assertions are not given in full generality.…”

“…We have a splitting extension K = L ⊕ M, where M is a nilpotent ideal of nilpotence degree ≤ n and an L-L-bimodule. In [20], automorphisms of such rings K are represented by certain matrices of order 2. It is done like this.…”