Structure of split additively orthodox semirings

Kaiqing Huang; Yizhi Chen; Aiping Gan; Kaiqing Huang; Yizhi Chen; Aiping Gan

doi:10.3934/math.2022633

AIMS Mathematics

2022, Volume 7, Issue 6: 11345-11361. doi: 10.3934/math.2022633

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Structure of split additively orthodox semirings

1.
Modern Industrial Innovation Practice Center, Dongguan Polytechnic, Dongguan 523808, China
2.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
3.
Department of Mathematics and Statistics, Huizhou University, Huizhou 516007, China
4.
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

Received: 12 January 2022 Revised: 01 April 2022 Accepted: 05 April 2022 Published: 12 April 2022
MSC : 16Y60, 20M10

The ideas of transversals are important to study algebraic structures which are useful for investigating semirings structure. In this paper, we introduce and explore split additively orthodox semirings which are special semirings with transversals. After obtaining some property theorems of split additively orthodox semirings, the structure theorem for them is obtained by using idempotent semirings, additively inverse semirings, and Munn semigroup. It not only extends and strengthens the corresponding results of Clifford semirings and split orthodox semigroups but also develops a new way to study semirings.
- split additively orthodox semiring,
- split idempotent semiring,
- additively inverse semiring,
- Munn semigroup
Citation: Kaiqing Huang, Yizhi Chen, Aiping Gan. Structure of split additively orthodox semirings[J]. AIMS Mathematics, 2022, 7(6): 11345-11361. doi: 10.3934/math.2022633

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Abstract

The ideas of transversals are important to study algebraic structures which are useful for investigating semirings structure. In this paper, we introduce and explore split additively orthodox semirings which are special semirings with transversals. After obtaining some property theorems of split additively orthodox semirings, the structure theorem for them is obtained by using idempotent semirings, additively inverse semirings, and Munn semigroup. It not only extends and strengthens the corresponding results of Clifford semirings and split orthodox semigroups but also develops a new way to study semirings.

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