Isomorphisms of certain locally nilpotent finitary groups and associated rings. (Q1876566)

Let \(K\) be a ring, \(X\) a totally ordered set and \(V\) a free \(K\)-module on the set \(X\). Endomorphisms of \(V\) can be described by row-finite matrices over \(K\) with rows and columns indexed by the ordered set \(X\). Let \(N(X,K)\) be the ring of all such matrices with zeros on and above the main diagonal and with non-zeros in only finitely many positions below. If either \(X\) is finite or \(K\) has no zero-divisors the authors describe the isomorphisms between \(N(X,K)\) and \(N(X',K')\) for \(X'\) a (possibly) second ordered set and \(K'\) a second ring. Their adjoint groups and associated Lie rings are also described.