Balanced Local Rings with Commutative Residue Fields by Vlastimil Dlab and Claus
نویسنده
چکیده
1. Let R be a ring with unity. An R-module M is said to be balanced or to have the double centralizer property, if the natural homomorphism from R to the double centralizer of M is surjective. If all left and right K-modules are balanced, R is called balanced. It is well known that every artinian uniserial ring is balanced. In [5], J. P. Jans conjectured that those were the only (artinian) balanced rings. Jans' conjecture has been shown to be false in [3] by constructing a class of balanced nonuniserial rings. In the present paper, we show that the rings of [3] together with the (local) uniserial rings are the only balanced rings which are local (i.e. have a unique one-sided maximal ideal) and whose residue division ring R/W is commutative (here, as well as in what follows, W denotes always the radical of R).
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