JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 101-108.doi: 10.6040/j.issn.1671-9352.0.2024.038

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Subvarieties based on the semiring Greens relation in COS·n

WANG Aifa, HU Yu   

  1. School of Mathematical Sciences, Chongqing University of Technology, Chongqing 400054, China
  • Published:2025-11-11

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Abstract: The Green's relations(·overL)∨D+,(·overL)∨L+,(·overL)∨R+, L+∨(·overD)of semirings are studied, and equivalent characterizations for these relations within semirings are provided. The necessary and sufficient conditions for these relations to constitute congruences are obtained. It is proven that the semiring classes determined by the aforementioned congruence relation are subvarieties. The Mal'cev product decomposition of these subvarieties is given.

Key words: semiring, Green relations, Mal'cev product, variety

CLC Number: 

  • O153.3
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