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<p>In the present paper, we introduce the <i>S</i>-quasi-Zariski topology on the <i>S</i>-quasi-primary spectrum of a commutative semiring and study its topological properties such as irreducibility, compactness and connectedness. We prove that the <i>S</i>-quasi-primary spectrum of a commutative semiring with the <i>S</i>-quasi-Zariski topology is a spectral space if and only if it is a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-space. The main results of the paper improve, generalize and correct the previous ones obtained for a commutative ring.</p>

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S-Quasi-Zariski topology on the S-quasi-primary spectrum of a commutative semiring

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Song-Chol Han,
  • Sin-Song Kim

摘要

In the present paper, we introduce the S-quasi-Zariski topology on the S-quasi-primary spectrum of a commutative semiring and study its topological properties such as irreducibility, compactness and connectedness. We prove that the S-quasi-primary spectrum of a commutative semiring with the S-quasi-Zariski topology is a spectral space if and only if it is a \(T_{0}\) T 0 -space. The main results of the paper improve, generalize and correct the previous ones obtained for a commutative ring.