Maximal regular right ideal space of a primitive ring. II

Authors:
Kwangil Koh and Hang Luh

Journal:
Trans. Amer. Math. Soc. **180** (1973), 127-141

MSC:
Primary 16A20

DOI:
https://doi.org/10.1090/S0002-9947-1973-0338049-8

MathSciNet review:
0338049

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0338049-8

Keywords:
Maximal regular right ideals,
socle,
irreducible spaces,
compact Hausdorff spaces,
lines,
hyperplanes,
support

Article copyright:
© Copyright 1973
American Mathematical Society