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Finite Dimension in Associative Rings
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  • Journal title : Kyungpook mathematical journal
  • Volume 48, Issue 1,  2008, pp.37-43
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2008.48.1.037
 Title & Authors
Finite Dimension in Associative Rings
Bhavanari, Satyanarayana; Dasari, Nagaraju; Subramanyam, Balamurugan Kuppareddy; Lungisile, Godloza;
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The aim of the present paper is to introduce the concept "Finite dimension" in the theory of associative rings R with respect to two sided ideals. We obtain that if R has finite dimension on two sided ideals, then there exist uniform ideals of R whose sum is direct and essential in R. The number n is independent of the choice of the uniform ideals and `n` is called the dimension of R.
ring;two sided ideal;essential ideal;uniform ideal;
 Cited by
M. R. Adhikari, Groups, Rings and Modules with Applications, University Press (India) Ltd., Hyderabad, India, 1999.

A. W. Goldie, The Structure of Noetherian Rings, Lectures on Rings and Modules, Springer-Verlag, New York, 1972.

I. N. Herstein, Topics in Algebra (Second Edition), Wiley Eastern Limited, New Delhi, 1998.

Y. V. Reddy and Bh. Satyanarayana, A Note on Modules, Proc. of the Japan Academy, 63-A(1987), 208-211.

Bh. Satyanarayana, A note on E-direct and S-inverse Systems, Proc. of the Japan Academy, 64-A(1988), 292-295.

Bh. Satyanarayana, K. Syam Prasad and D. Nagaraju, A Theorem on Modules with Finite Goldie Dimension, Soochow J. Maths 32(2)(2006), 311-315.