By J. L. S. Chen, N. Q. Ding

The chosen papers during this quantity hide the entire most vital parts of ring idea and module idea comparable to classical ring thought, illustration idea, the idea of quantum teams, the speculation of Hopf algebras, the speculation of Lie algebras and Abelian workforce conception. The overview articles, written by means of experts, supply a great assessment of a few of the components of ring and module thought - excellent for researchers searching for a brand new or comparable box of analysis. additionally incorporated are unique articles displaying the craze of present examine.

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7]) Let R a semiprime ring. If R and a ring S are Morita equivalent, then Qq~~ 1. Then Q~~~~
~~

Therefore, c = (d^ , • • • , d^, z' , z , • • • )a £ Ra. Ra. Hence, ^? is left morphic. 1. R[D,D] is a left morphic ring if and only if D is a left morphic ring. 1. Let R = R[D,C] where D = M 2 (Z 2 ) and C = {(%") : x,y 6 Zz}. Then the following hold: (1) (2) (3) (4) R R R R is a morphic ring. is semiprimitive. is left and right nonsingular. is not regular. Proof. (1). ) or (J {), let b = (° g); If a = (° J), let 6 = (° J). In either case, we have lc(a) = Cb, lc(&) = Co, ID (a) = Db, lD(b) = Da and r c (a) = bC, rc(b) = aC, rD(a) = bD, rD(b) = aD.

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.