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Let C be a commutative Dedekind domain, let S be a maximal C-order in a simple Artinian ring Q, and let K be a proper essential right ideal of S with SK=S. We shall study those maximal C-orders in Q which contain the idealiser ring R of K and the way in which invertible ideals of R act on them by conjugation. In a special case, which includes that in which R is hereditary, we shall show that these...
We construct many pairwise non-isomorphic maximalZ-ordersAandBwhich have isomorphicnbynmatrix rings for every positive integern≠1. In most casesAalso has the property that every one-sided ideal ofM 2 (A) is principal but not every one-sided ideal ofAis principal.