TY - JOUR
T1 - ON THE FINITE GOLDIE DIMENSION OF SUM OF TWO IDEALS OF AN R-GROUP
AU - Sahoo, Tapatee
AU - Kedukodi, Babushri Srinivas
AU - Harikrishnan, Panackal
AU - Kuncham, Syam Prasad
N1 - Publisher Copyright:
© 2023 Sciendo. All rights reserved.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
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U2 - 10.7151/dmgaa.1419
DO - 10.7151/dmgaa.1419
M3 - Article
AN - SCOPUS:85179487183
SN - 1509-9415
VL - 43
SP - 177
EP - 187
JO - Discussiones Mathematicae - General Algebra and Applications
JF - Discussiones Mathematicae - General Algebra and Applications
IS - 2
ER -