A stucture sheaf for semiprime rings
作者:
I.B. Rumbos,
期刊:
Communications in Algebra
(Taylor Available online 1989)
卷期:
Volume 17,
issue 11
页码: 2773-2794
ISSN:0092-7872
年代: 1989
DOI:10.1080/00927878908823874
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
For any ring R (associative with 1) we associate a space X of prime torsion theories endowed with Golan's SBO-topology. A separated presheaf (L-,M) on X is then constructed for any right R-module MR, and a sufficient condition on M is given P such that L(-, M ) i s actually a sheaf. The sheaf spacedetermined by L(-,M) represents M i n the following sense: M is isomorphic to the module of continuous global sections of p.These results are applied to the right R-module RRand it is seen that semiprime rings satisfy the required condition for L(-, R ) to be a sheaf. Among semiprime rings two classes are sin- gled out, fully symmetric semiprime and right noetherian semiprime rings; these two kinds of rings have the desirable property of yielding “nice” stalks for the above sheaf.
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