JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 1-7.doi: 10.6040/j.issn.1671-9352.0.2020.453

   

Semiring varieties defined by Greens relations on a semiring

CHENG Yan-liang, SHAO Yong*   

  1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China
  • Published:2021-04-13

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Abstract: The properties and characterizations of congruence openings determined by Greens relations of a semiring are given. We obtain that several classes of semirings by means of these congruence openings, prove that these classes of semirings are varieties of semirings, and uncover relationships between these varieties. By exploring opening operators on the lattice of all subvarieties of varieties of semirings, the order embedding theorem of the lattice of all subvarieties of the variety of multiplicatively idempotent semirings into the direct product of the lattice of open varieties is given.

Key words: semiring, Greens relation, congruence opening, opening operator, variety of semirings

CLC Number: 

  • O151.21
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