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<p>We study several properties and applications of the <i>S</i>-Noetherian rings and modules. It is proved that an <i>S</i>-Artinian ring is <i>S</i>-Noetherian provided that <i>S</i> contains no zero divisors of the module. Furthermore, it is shown that associated primes exist in modules over the <i>S</i>-Noetherian rings and the major part of notions of associated prime ideals coincide over the <i>S</i>-Noetherian rings. We also extend the classical Krull’s intersection theorem for <i>S</i>-Noetherian rings. Moreover, we provide a characterization of the <i>S</i>-Noetherian modules in terms of the <i>G</i>-graded <i>S</i>-Noetherian modules.</p>

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Some Remarks on S-Noetherian Modules

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Ajim Uddin Ansari,
  • Sanjeev Kumar Maurya,
  • B. K. Sharma

摘要

We study several properties and applications of the S-Noetherian rings and modules. It is proved that an S-Artinian ring is S-Noetherian provided that S contains no zero divisors of the module. Furthermore, it is shown that associated primes exist in modules over the S-Noetherian rings and the major part of notions of associated prime ideals coincide over the S-Noetherian rings. We also extend the classical Krull’s intersection theorem for S-Noetherian rings. Moreover, we provide a characterization of the S-Noetherian modules in terms of the G-graded S-Noetherian modules.