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

Alaa Abouhalaka () and Şehmus Fındık
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Alaa Abouhalaka: Department of Mathematics, Çukurova University, Balcalı, Adana 01330, Turkey
Şehmus Fındık: Department of Mathematics, Çukurova University, Balcalı, Adana 01330, Turkey

Mathematics, 2023, vol. 11, issue 8, 1-12

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.

Keywords: almost right primary ideals; almost nilary ideals; noncommutative rings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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