Geodesic
On the finite Goldie dimension of sum of two ideals of an R-group
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 177-187

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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 (Ω-FGD), if K_1, K_2 are ideals of G wherein K_1∩ K_2 is an Ω-complement, then dim_Ω(K_1+K_2)=dim_Ω(K_1)+ dim_Ω(K_2)-dim_Ω(K_1∩ K_2). In the sequel, we prove several properties.
Keywords: nearring, essential ideal, uniform ideal, finite dimension 
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Sahoo, Tapatee; Kedukodi, Babushri Srinivas; Harikrishnan, Panackal; Kuncham, Syam Prasad. On the finite Goldie dimension of sum of two ideals of an R-group. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 177-187. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a0/