TL;DR
This paper explores local loop near-rings, a generalization of near-rings with non-associative addition, introducing the concept of localness and providing a detection principle for it.
Contribution
It introduces the concept of local loop near-rings and establishes a detection principle for their localness, expanding the theory of near-rings.
Findings
Defined local loop near-rings.
Proved a detection principle for localness.
Extended near-ring theory to non-associative cases.
Abstract
We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.
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