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Finite Dimension in Associative Rings

Bhavanari, Satyanarayana;Dasari, Nagaraju;Subramanyam, Balamurugan Kuppareddy;Lungisile, Godloza

  • Received : 2006.07.06
  • Published : 2008.03.31

Abstract

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 $U_1,U_2,\ldots,U_n$ of R whose sum is direct and essential in R. The number n is independent of the choice of the uniform ideals $U_i$ and 'n' is called the dimension of R.

Keywords

ring;two sided ideal;essential ideal;uniform ideal

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