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Extra info for Advances in Ring Theory - Proceedings of: Proceedings of the 4th China-Japan-Korea International Conference, Nanjing, China 24-28 June 2004
L. Osofsky, Personal Communication to S. T. Rizvi, Summer, 2003. 35. M. M. Parmenter and Y. Zhou, Finitely S-CS property of excellent extensions of rings, Algebra Colloq. 10 (2003), 17-21. 36. D. S. Passman, The Algebraic Structure of Group Rings, Wiley, New York, 1977. 37. A. Pollingher and A. Zaks, On Baer and quasi-Baer rings, Duke Math. J. 37 (1970), 127-138. 38. C. E. Rickart, Banach algebras with an adjoint operation, Ann. Math. 47 (1946), 528-550. 39. Y. Utumi, On quotient rings, Osaka Math.
L. Osofsky, On ring properties of injective hulls, Canad. Math. Bull. 7 (1964), 405-413. 33. B. L. Osofsky, A non-trivial ring with non-rational injective hull, Canad. Math. Bull. 10 (1967), 275-282. 34. B. L. Osofsky, Personal Communication to S. T. Rizvi, Summer, 2003. 35. M. M. Parmenter and Y. Zhou, Finitely S-CS property of excellent extensions of rings, Algebra Colloq. 10 (2003), 17-21. 36. D. S. Passman, The Algebraic Structure of Group Rings, Wiley, New York, 1977. 37. A. Pollingher and A.
It follows that lr>(ai) 2 Dbi and ID (61) 2 Dai. R. Then d € l#(a) = #6, showing that s £ Dbi. Therefore, lr»(oi) = Dbi. Similarly, lD(bi) = Dai. So D is a left morphic ring. To show condition (2), let x £ C and let a = (x, x, • • • ) £ R. R&, and 1^(6) = Ra. It follows that lc(x) 2 Cy, lc(y) 2 Cx, lD(x) 2 Dy, and lD(y) D Dx. b, showing that s £ Cy; thus lc(^) = Cy. If t e lc (y), let c = (cj) e /? ,- = £ for j > n. Then c 6 \n(b) = -Ra, showing that t € Cx; hence lc(y) = Cx. R with di = • • • = dn+i = u and dj = 0 for j > n + 1.