Finite Dimension in Associative Rings

• 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;

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 $\small{U_1,U_2,\ldots,U_n}$ of R whose sum is direct and essential in R. The number n is independent of the choice of the uniform ideals $\small{U_i}$ and 'n' is called the dimension of R.
Keywords
ring;two sided ideal;essential ideal;uniform ideal;
Language
English
Cited by
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