Formal Matrix Rings Research Articles

A class of formal matrix rings

This paper concerns the formal matrix ring Mn(R;s) over a ring R defined by a central element s in R. Various basic properties of these rings are established; the isomorphism problem between these rings is addressed; some known results on the usual matrix rings are extended to the formal matrix rings; and the Cayley–Hamilton Theorem is proved for matrices in a formal matrix ring.

On K 2-group of a formal matrix ring

Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show that K2(s)≃K2(T)⊕K2(S, I), and a presentation of K2(S, I) is given.

Modules over formal matrix rings

This work contains some new and known results on modules over formal matrix rings. The main results are presented with proofs.