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On the Dimension of the Quotient Ring R/K Where K is a Complement

Satyanarayana Bhavanari, Nagaraju Dasari, Babu Prasad Munagala, Mohiddin Shaw Shaik

Pages - 16 - 22 | Revised - 31-01-2011 | Published - 08-02-2011

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KEYWORDS

Collision, Risk, Inland Waterways, Environmental Prevention

ABSTRACT

The aim of the present paper is to obtain some interesting results related to the concept “finite dimension” in the theory of associative rings R with respect to two sided ideals. It is known that if an ideal H of R has finite dimension, then there exist uniform ideals Ui, 1 i n of R such that the sum U1 U2 … Un is essential in H. This n is independent of choice of uniform ideals and we call it as dimension of H (we write dim H, in short). We obtain some important relations between the concepts complement ideals and essential ideals. Finally, we proved that dim(R/K) = dim R – dim K for a complement ideal K of R. We include some necessary examples.

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Mr. Satyanarayana Bhavanari

- India

bhavanari2002@yahoo.co.in

Dr. Nagaraju Dasari

- India

Dr. Babu Prasad Munagala

- India

Mr. Mohiddin Shaw Shaik

- India