On the binary system of factors of formal matrix rings

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz

On Realization and Isomorphism Problems for Formal Matrix Rings

“…Sufficiency. Principal multiplier matrices for the rings K 1 and K 2 uniquely define all remaining multiplier matrices, see [5,Lemma 4.7]. Therefore, we can repeat the argument from the proof of Theorem 4.1(2).…”

“…The matrix S is symmetrical. Following [5], we call it a principal multiplier matrix. In [5], the matrices (s ijk ) and (s kij ) are also used, k = 1, .…”

“…Namely, the realization problem I and the isomorphism problem III. These problems are considered in [1], [2], [5], [12], [13].…”

“…Remark 4.4. In [5,Theorem 4.12], a result, which is similar to Theorem 4.3, is proved for a left Artinian ring R.…”

“…Relationships between the rings M(n, R, s) and crossed matrix ring are known (see [4]). In [5,Lemma 4.7], it is proved that the principal multiplier of the matrix ring M(n, R, s) determines all other multiplier matrices. For (01)-formal matrix rings, a similar assertion does not appear to be true.…”