## 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 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.

Original language | English |
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Pages (from-to) | 177-187 |

Number of pages | 11 |

Journal | Discussiones Mathematicae - General Algebra and Applications |

Volume | 43 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2023 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Applied Mathematics