On Union of Regular Near-rings
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911047104856064 |
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| author | Mukherjee, Rajlaxmi Manna, Tuhin Chakraborty, Kamalika Sardar, Sujit Kumar |
| author_facet | Mukherjee, Rajlaxmi Manna, Tuhin Chakraborty, Kamalika Sardar, Sujit Kumar |
| contents | '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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_06572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Union of Regular Near-rings Mukherjee, Rajlaxmi Manna, Tuhin Chakraborty, Kamalika Sardar, Sujit Kumar Rings and Algebras 16Y30, 16Y60, 16Y99 '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. |
| title | On Union of Regular Near-rings |
| topic | Rings and Algebras 16Y30, 16Y60, 16Y99 |
| url | https://arxiv.org/abs/2507.06572 |