DOI: 10.54974/fcmathsci.1914514 ISSN: 2717-6185

Soft N-Clogroups over Near-Rings and Their Extended Operations

İncinur Yılmaz, Emin Aygun
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In this paper, we introduce the notion of a soft N -clogroup over a near-ring by combining the classical concept of N -clogroups with soft set theory. This framework provides a parameter-dependent extension of the subgroup-generation mechanism induced by multiplicative action in near-rings. We define soft N -clogroups and soft sub-N -clogroups and present illustrative examples clarifying their structural behavior. We further investigate the behavior of these structures under extended union and extended intersection operations. The associativity of these extended operations is established within the soft N - clogroup framework. The obtained results provide a systematic structural analysis of soft N -clogroups and clarify the behavior of extended operations in this setting. Moreover, we examine the behavior of soft N -clogroups under near-ring homomorphisms and show that preimages preserve the soft N -clogroup structure, whereas homomorphic images do not necessarily preserve it.

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