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Open Access Research Article

Fully Stable Semirings and Related Concepts

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pp. 1025–1030Vol. 28Issue 4-AJune 2025DOI: 10.47974/JDMSC-2028 Crossmark XML
Received:
09 Jul 2024
Published Online:
26 Jun 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2028
Pages:
1025–1030

Abstract

In this article, we introduce the notion of fully stable semiring. Several equivalent definitions of this concept exist, and numerous classical constructs satisfy a fully stable semiring, such as the 2-regular semiring. A relation ΨK has been observed on a semiring K, which is evidence of stability. Upon further investigation of this concept, a stronger concept emerged depending on annihilator ideal θ, which is called fully θ-stable; the properties of this concept provided a most important property: ‘any ideal in a commutative fully θ-stable semiring possesses a unique complement ideal.’

Keywords

Subject Classifications

Primary 06E20Secondary 13C60

References

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