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Locally compact topologically nil and monocompact PI-rings. (English) Zbl 0973.16026

The following results are proved in the article: A locally compact compactly generated monocompact PI-ring is compact; A locally compact compactly generated topologically nil PI-ring is projectively nilpotent; There is no non-discrete locally compact simple nil ring equipped with a minimal ring topology; There is no non-discrete locally compact simple nil ring with nonzero characteristic and with self dual additive group.

MSC:

16W80 Topological and ordered rings and modules
54H13 Topological fields, rings, etc. (topological aspects)
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16R99 Rings with polynomial identity
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