Maximal regular right ideal space of a primitive ring. II
Authors:
Kwangil Koh and Hang Luh
Journal:
Trans. Amer. Math. Soc. 180 (1973), 127141
MSC:
Primary 16A20
MathSciNet review:
0338049
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Abstract: If is a ring, let be the set of maximal regular right ideals of . For each nonempty subset of , define the hull of to be the set and the support of to be the complement of the hull of . Topologize by taking the supports of right ideals of as a subbase. If is a right primitive ring, then is homeomorphic to an open subset of a compact space of a right primitive ring , and is a discrete space if and only if is a compact Hausdorff space if and only if either is a finite ring or a division ring. Call a closed subset of a line if is the hull of for some two distinct elements and in . If is a semisimple ring, then every line contains an infinite number of points if and only if either is a division ring or is a dense ring of linear transformations of a vector space of dimension two or more over an infinite division ring such that every pair of simple (right) modules are isomorphic.
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 J. von Neumann, On regular rings, Proc. Nat. Acad. Sci. U. S. A. 22 (1936), 707713.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197303380498
PII:
S 00029947(1973)03380498
Keywords:
Maximal regular right ideals,
socle,
irreducible spaces,
compact Hausdorff spaces,
lines,
hyperplanes,
support
Article copyright:
© Copyright 1973
American Mathematical Society
