Abstract
Let R be a ring with unity. An R-module M is called balanced, the natural homomorphism from R to the double centralizer of M is surjective. If every left R-module is balanced, R is said to be left balanced (or to satisfy the double centralizer condition for left modules). It is well-known that every artinian uniserial ring is both left and right balanced, and recently Jans [3] conjectured that if R has minimum condition, then every R-module has the double centralizer condition and only R is a uniserial ring. This conjecture has been proved in [-1] to be true for rings which are finitely generated over their centres. However, the following theorem shows that, in general, the conjecture is false.
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