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On a problem of Bertram Yood

Mart Abel, Mati Abel (2014)

Topological Algebra and its Applications

In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.

On a subset with nilpotent values in a prime ring with derivation

Vincenzo De Filippis (2002)

Bollettino dell'Unione Matematica Italiana

Let R be a prime ring, with no non-zero nil right ideal, d a non-zero drivation of R , I a non-zero two-sided ideal of R . If, for any x , y I , there exists n = n x , y 1 such that d x , y - x , y n = 0 , then R is commutative. As a consequence we extend the result to Lie ideals.

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