On Union of Regular Near-rings

Rajlaxmi Mukherjee; Tuhin Manna; Kamalika Chakraborty; Sujit Kumar Sardar

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arXiv · 2507.06572

On Union of Regular Near-rings

Rajlaxmi Mukherjee·Tuhin Manna·Kamalika Chakraborty·Sujit Kumar Sardar

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Abstract

'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup Forum (2018)]. In it, a class of seminearrings (called generalized left completely regular seminearrings, abbreviated as GLCR) has been characterized as a union of near-rings. This work has been extended in the present article to characterize the seminearrings which are union of various types (regular, completely regular, inverse, Clifford) of regular near-rings.

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Rajlaxmi Mukherjee, Tuhin Manna, Kamalika Chakraborty, Sujit Kumar Sardar. 2025-07-09. On Union of Regular Near-rings. https://arxiv.org/abs/2507.06572

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