ON THE FINITE GOLDIE DIMENSION OF SUM OF TWO IDEALS OF AN R-GROUP

Document Type

Article

Publication Title

Discussiones Mathematicae - General Algebra and Applications

Abstract

We consider an R-group G, where R is a zero symmetric right nearring. We obtain the Ω-dimension of sum of two ideals of G, as a natural generalization of sum of two subspaces of a finite dimensional vector space; indeed, difficulty due to non-linearity in G. However, in this paper we overcome the situation under a suitable assumption. More precisely, we prove that for a proper ideal Ω of G with Ω-finite Goldie dimension (ΩF GD), if K1, K2 are ideals of G wherein K1 ∩ K2 is an Ω-complement, then dimΩ(K1 + K2) = dimΩ(K1) + dimΩ(K2) − dimΩ(K1 ∩ K2). In the sequel, we prove several properties.

First Page

177

Last Page

187

DOI

10.7151/dmgaa.1419

Publication Date

1-1-2023

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