JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 45-48.doi: 10.6040/j.issn.1671-9352.0.2021.157

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The property and structure of left Clifford bi-semirings

WEI Meng-jun, LI Gang*   

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, Shandong, China
  • Published:2021-08-09

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Abstract: The distributive lattice of bi-semirings and band bi-semirings are defined. Using these two definitions and the properties of the left Clifford semigroup, the definitions of the left bi-ring and the left Clifford bi-semiring are given. The necessary and sufficient conditions for a bi-semiring to be a left bi-ring and a bi-semiring to be a left Clifford bi-semiring are obtained.

Key words: band bi-semiring, left bi-ring, left Clifford bi-semiring, distributive lattice congruence

CLC Number: 

  • O152.7
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