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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 3

On Prime and Maximal k-Subsemimodules of Semimodules

Gürsel YEŞİLOT
Sayfa
305–312
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

After that, the correspondence between prime k-ideals andprime k-subsemimodules, and between maximal k-ideals and maximalk-subsemimodules are given.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we present some characterizations of prime k-ideals andmaximal k-ideals of a semiring.
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Temel Bulgular & Veri:Then we extend these properties toprime k-subsemimodules and maximal k-subsemimodules of a semimodule.
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Sonuç & Katkı:After that, the correspondence between prime k-ideals andprime k-subsemimodules, and between maximal k-ideals and maximalk-subsemimodules are given.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Prime k-ideal · Maximal k-ideal · Prime k-subsemimodule

Abstract

In this paper, we present some characterizations of prime k-ideals andmaximal k-ideals of a semiring. Then we extend these properties toprime k-subsemimodules and maximal k-subsemimodules of a semimodule. After that, the correspondence between prime k-ideals andprime k-subsemimodules, and between maximal k-ideals and maximalk-subsemimodules are given.

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Bu Makaleye Atıf Yap

YEŞİLOT, G. (2022). On Prime and Maximal k-Subsemimodules of Semimodules. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 3, 305–312. https://ajindex.com/articles/530857

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Kaynakça (8)

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  2. Allen, P. J. Neggers, J. and Kim, H. S. Ideal theory in commutative A-semirings, Kyungpook Math. J. 46, 261–271, 2006.
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  5. Chin-Pi Lu, C.-P. Unions of prime submodules, Houston J. Math. 23 (2), 203–213, 1997.
  6. Sen, M. K. and Adhikari, M. R. On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118(3), 699–703, 1993.
  7. Shabir, M. and Iqbal, M. S. One-sided prime ideals in semirings, Kyungpook Math. J. 47, 473–480, 2007.
  8. Weinert, H. J., Sen, M. K. and Adhikari, M. R. One-sided k-ideals and h-ideals in semirings, Math. Pannon. 7 (1), 147–162, 1996.