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Quasi S-n-ideals in commutative semirings

  • Amaresh Mahato
  • Saikat Das
  • Manasi Mandal
  • Sampad Das
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Abstract

Let R be a commutative semiring with unity (1≠0), and let S be a proper multiplicatively closed subset of R. In this paper, we introduce the notion of quasi S-n-ideals in commutative semirings. We the study basic property of quasi S-n-ideals and establish their relationships with quasi n-ideals, S-n-ideals, S-prime ideals, and S-primary ideals. We also investigate their behavior under localization. Finally, we determine quasi S-n-ideals in the quotient polynomial semiring R[x]/⟨ xm⟩ and study their natural extensions via the constructions of idealization and amalgamation.

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Cite

BibTeXRIS
BibTeX
@misc{mahato2026quasi,
  title = {{Quasi S-n-ideals in commutative semirings}},
  author = {Amaresh Mahato and Saikat Das and Manasi Mandal and Sampad Das},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03743},
  eprint = {2609.03743},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03743},
}
RIS
TY  - UNPB
TI  - Quasi S-n-ideals in commutative semirings
AU  - Amaresh Mahato
AU  - Saikat Das
AU  - Manasi Mandal
AU  - Sampad Das
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03743
UR  - https://arxiv.org/abs/2609.03743
AB  - Let R be a commutative semiring with unity (1≠0), and let S be a proper multiplicatively closed subset of R. In this paper, we introduce the notion of quasi S-n-ideals in commutative semirings. We the study basic property of quasi S-n-ideals and establish their relationships with quasi n-ideals, S-n-ideals, S-prime ideals, and S-primary ideals. We also investigate their behavior under localization. Finally, we determine quasi S-n-ideals in the quotient polynomial semiring R[x]/⟨ x^m⟩ and study their natural extensions via the constructions of idealization and amalgamation.
ER  -