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

The chosen papers during this quantity conceal the entire most crucial components of ring concept and module idea reminiscent of classical ring idea, illustration idea, the idea of quantum teams, the speculation of Hopf algebras, the speculation of Lie algebras and Abelian crew idea. The assessment articles, written via experts, supply an outstanding review of some of the components of ring and module conception - perfect for researchers trying to find a brand new or comparable box of research. additionally integrated are unique articles exhibiting the fashion of present study.

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**Sample text**

6]) Assume that R is a semiprime ring and n is a positive integer. )), where B. 3, or We note that the statement of Theorem 17 does not hold true when ^ = q<£. To show this, let K be a field and n be a positive integer such that n > 1. Then as shown in [9], the ring Ma,tn(K[x}) = Matn(K)[x] is not right quasi-continuous. tn(K))[x]). Thus Q^(Matn(K)[x]) ^ Q q e(Mat n (A"))[x]. tn(K[x])) ^ M&tn(K[x])(= Main(Qqe:(K[x])'). Hence Also we see that Theorem 17 does not hold for the case when ^ = 03 21 or ^ = £.

We prove that R[D, C] is strongly left morphic; it is similar to show that R[D,C] is strongly right morphic. By Lemma 5, we only need to show that R[Mn(D),Mn(C)] is left morphic for all n > 1. Since Mn(£>) is clearly left morphic, it suffices to show that every 0 ^ A = (ajj) € M n (C) is left [Mn(£>),Mn(C')]-morphic by Theorem 1. Note that C = {(o 0)1 (o i)> (o i)> (o o)}If Of, is a unit of C for some i and j, interchanging the 1th and zth rows and interchanging the 1th and jth columns will bring ay- to the (1, l)-entry.

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. 21. K. R. Goodearl, Von Neumann regular rings: Connections with functional analysis, Bull. Amer. Math. Soc. ) 4 (1981), 125-134. 22. K. R. Goodearl, Simple Noetherian rings not isomorphic to matrix rings over domains, Comm. Algebra 12 (1984), 1412-1434. 23. Y. Hirano, M. Hongan and M. P.