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Extension of Almost Primary Ideals to Noncommutative Rings and the Generalization of Nilary Ideals

Author

Listed:
  • Alaa Abouhalaka

    (Department of Mathematics, Çukurova University, Balcalı, Adana 01330, Turkey
    These authors contributed equally to this work.)

  • Şehmus Fındık

    (Department of Mathematics, Çukurova University, Balcalı, Adana 01330, Turkey
    These authors contributed equally to this work.)

Abstract

In this paper, we introduce the concepts of almost right primary ideals and almost nilary ideals and study their related results. We compare almost right primary ideals with other types of ideals, such as right primary ideals and weakly right primary ideals, and investigate their forms in decomposable rings. Moreover, we study the prime radical of an ideal of the product rings. Finally, we provide a definition of fully almost right primary rings and demonstrate that the homomorphic image of a fully almost right primary ring is again a fully almost right primary ring. We also investigate the quotient structure of fully almost right primary rings.

Suggested Citation

  • Alaa Abouhalaka & Şehmus Fındık, 2023. "Extension of Almost Primary Ideals to Noncommutative Rings and the Generalization of Nilary Ideals," Mathematics, MDPI, vol. 11(8), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1917-:d:1126775
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