On additively completely regular seminearrings |
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| Authors: | Rajlaxmi Mukherjee Pavel Pal |
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| Institution: | 1. Department of Mathematics, Garhbeta College, Garhbeta, Paschim Medinipur, India;2. Department of Mathematics, Jadavpur University, Kolkata, India |
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| Abstract: | In an attempt to investigate the situation arising out of replacing additive regularity by additive complete regularity in our previous study on additively regular seminearrings, we introduce the notions of left (right) completely regular seminearrings and characterize left (right) completely regular seminearrings as bi-semilattices of left (resp., right) completely simple seminearrings. We also define left (right) Clifford seminearrings and show that they are precisely bi-semilattices of near-rings (resp., zero-symmetric near-rings). |
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| Keywords: | Additively completely regular seminearring Green’s relation left (right) Clifford seminearring left (right) completely regular seminearring left (right) completely simple seminearring |
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