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

The chosen papers during this quantity disguise all of the most crucial components of ring idea and module thought akin to classical ring idea, illustration conception, the speculation of quantum teams, the speculation of Hopf algebras, the speculation of Lie algebras and Abelian crew idea. The overview articles, written via experts, supply a very good evaluation of some of the parts of ring and module conception - excellent for researchers searching for a brand new or comparable box of analysis. additionally integrated are unique articles exhibiting the craze of present learn.

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445] it is also shown that for any ring R, CRFMr(-R) is never right extending when F is countably infinite. 7], and Theorem 20(i) yield that CRFM r (Q q2 j(fl)) exists and is right Fl-extending. Hence with each semiprime ring we can associate a right Fl-extending ring which is not right extending. For a given 22 nonempty set F, we remark that R is quasi-Baer if and only if the column finite F x F upper triangular matrix ring is quasi-Baer as was shown in [16]. From Theorems 17 and 20, one might expect that either or y q or <5 q **
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J. Doh, H. L. Jin and J. K. Park, Quasi-Baer rings with essential prime radicals, Preprint 17. N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, Longman, Harlow, 1994. 18. C. Faith and Y. Utumi, Maximal quotient rings, Proc. Araer. Math. Soc. 16 (1965), 1084-1089. 19. M. Ferrero, Closed submodules of normalizing bimodules over semiprime rings, Comm. Algebra 29 (2001), 1513-1550. 20. K. R. Goodearl, Ring Theory: Nonsingular Rings and Modules, Marcel Dekker, New York, 1976.

1. Let C be a subring of a ring D. Then Mn(R[D,C]) R[Mn(D),Un(Q] Proof. W 1 \ r 211 \X22> = defined by C ln) (r^h x \ 2n) 12 2n is the required ring isomorphism. D For convenience, we introduce the following definition. 1. Let C be a subring of a ring D. An element a; £ C is called left [D,(7]-morphic if there exists y e C such that lc(z) = Cy, 1<7 (y) = Cx, ID (a;) = Dy, and \r>(y) — Dx. In this case, we say that x is left [P^j-morphic to y. 2. Let C be a subring of a ring D and let x € C be a left [D, C]-morphic element.