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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 Sayı: 3

Properties of the subtractive prime spectrum of a semimodule

Song-chol HAN
Won-jin HAN
Won-sok PAE
Sayfa
546–559
Yayın Tarihi
2023-05-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

For a multiplication semimodule over a commutative semiring, we prove that the radical of a subtractive subsemimodule coincides with its subtractive radical, that every proper subtractive subsemimodule is contained in a subtractive prime subsemimodule, that the multiplication semimodule is subtractively finitely generated iff its subtractive prime spectrum is a compact space, that in the subtractive prime spectrum, the intersection of finitely many basic open sets is compact, and that the subtractive prime spectrum of the subtractively finitely generated multiplication semimodule is a spectral space.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:For a top semimodule over a semiring with zero and nonzero identity, this paper studies the interplay between topological properties of the subtractive prime spectrum and algebraic properties of the semimodule.
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Temel Bulgular & Veri:We prove that the subtractive prime spectrum of the subtractively finitely generated top semimodule is a compact space, and establish necessary and sufficient conditions for the top semimodule to be subtractively finitely generated.
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Sonuç & Katkı:For a multiplication semimodule over a commutative semiring, we prove that the radical of a subtractive subsemimodule coincides with its subtractive radical, that every proper subtractive subsemimodule is contained in a subtractive prime subsemimodule, that the multiplication semimodule is subtractively finitely generated iff its subtractive prime spectrum is a compact space, that in the subtractive prime spectrum, the intersection of finitely many basic open sets is compact, and that the subtractive prime spectrum of the subtractively finitely generated multiplication semimodule is a spectral space.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Semiring · semimodule · prime subsemimodule

Abstract

For a top semimodule over a semiring with zero and nonzero identity, this paper studies the interplay between topological properties of the subtractive prime spectrum and algebraic properties of the semimodule. We prove that the subtractive prime spectrum of the subtractively finitely generated top semimodule is a compact space, and establish necessary and sufficient conditions for the top semimodule to be subtractively finitely generated. For a multiplication semimodule over a commutative semiring, we prove that the radical of a subtractive subsemimodule coincides with its subtractive radical, that every proper subtractive subsemimodule is contained in a subtractive prime subsemimodule, that the multiplication semimodule is subtractively finitely generated iff its subtractive prime spectrum is a compact space, that in the subtractive prime spectrum, the intersection of finitely many basic open sets is compact, and that the subtractive prime spectrum of the subtractively finitely generated multiplication semimodule is a spectral space.

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Bu Makaleye Atıf Yap

HAN, S., HAN, W., PAE, W. (2023). Properties of the subtractive prime spectrum of a semimodule. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 Sayı: 3, 546–559. https://ajindex.com/articles/939770

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