Contributions to Algebra and Geometry

38(2), 233-239 (1997)

Department of Mathematics,

National Cheng-Kung University, Tainan, Taiwan

**Abstract:** Rings with zero total and bounded indices are characterized. It is proved that essential left (right) ideals of such rings contain essential two sided ideals generated by central idempotents. In particular, a prime ring with bounded indices has zero total if and only if it is a matrix ring over a skew field. It is shown that the maximal right ring of quotients of a such ring is equal to the maximal left ring of quotients and is isomorphic to finite direct sum of matrix rings over abelian regular self\ts injective rings.

**Keywords:** idempotent, total, index of nilpotency, ring of quotients

**Classification (MSC91):** 16E50, 16S90

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