On prime spectrums of 2-primal rings
by C. Selvaraj   S. Petchimuthu  

Vol. 6 No. 1 (2011) P.73~P.84

ABSTRACT

A $2$-primal ring is one in which the prime radical is exactly the set of nilpotent elements. A ring is clean, provided every element is the sum of a unit and an idempotent. Keith Nicholson introduced clean rings in 1977 and proved the following: ``Every clean ring is an exchange ring. Conversely, every exchange ring in which all idempotents are central, is clean.'' In this paper, we investigate some of the relationships among ring-theoretic properties and topological conditions, such as a $2$-primal weakly exchange ring and its prime spectrum Spec$(R).$

KEYWORDS
Exchange rings, spectrum, strongly zero-dimensional, zero-dimensional

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 13A15, 06F25

MILESTONES

Received: 2009-06-30
Revised : 2009-11-17
Accepted: 2009-11-17

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