The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in Rings
In this paper, we prove that the characteristic of a minimal ideal and a minimal generalized ideal, which is meant to be one of minimal left ideal, minimal right ideal, bi-ideal, quasi-ideal, and m,n-ideal in a ring, is either zero or a prime number p. When the characteristic is zero, then the minim...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2023/6478767 |
| _version_ | 1827009799172128768 |
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| author | Rigena Sema Petraq Petro Kostaq Hila |
| author_facet | Rigena Sema Petraq Petro Kostaq Hila |
| author_sort | Rigena Sema |
| collection | DOAJ |
| description | In this paper, we prove that the characteristic of a minimal ideal and a minimal generalized ideal, which is meant to be one of minimal left ideal, minimal right ideal, bi-ideal, quasi-ideal, and m,n-ideal in a ring, is either zero or a prime number p. When the characteristic is zero, then the minimal ideal (minimal generalized ideal) as additive group is torsion-free, and when the characteristic is p, then every element of its additive group has order p. Furthermore, we give some properties for minimal ideals and for generalized ideals which depend on their characteristics. |
| first_indexed | 2024-04-09T20:10:49Z |
| format | Article |
| id | doaj.art-4d9f54e328d641b09a1635c96c7cdf04 |
| institution | Directory Open Access Journal |
| issn | 1687-0425 |
| language | English |
| last_indexed | 2025-02-18T12:54:45Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj.art-4d9f54e328d641b09a1635c96c7cdf042024-11-02T03:57:37ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences1687-04252023-01-01202310.1155/2023/6478767The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in RingsRigena Sema0Petraq Petro1Kostaq Hila2Department of MathematicsDepartment of MathematicsDepartment of Mathematical EngineeringIn this paper, we prove that the characteristic of a minimal ideal and a minimal generalized ideal, which is meant to be one of minimal left ideal, minimal right ideal, bi-ideal, quasi-ideal, and m,n-ideal in a ring, is either zero or a prime number p. When the characteristic is zero, then the minimal ideal (minimal generalized ideal) as additive group is torsion-free, and when the characteristic is p, then every element of its additive group has order p. Furthermore, we give some properties for minimal ideals and for generalized ideals which depend on their characteristics.http://dx.doi.org/10.1155/2023/6478767 |
| spellingShingle | Rigena Sema Petraq Petro Kostaq Hila The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in Rings International Journal of Mathematics and Mathematical Sciences |
| title | The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in Rings |
| title_full | The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in Rings |
| title_fullStr | The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in Rings |
| title_full_unstemmed | The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in Rings |
| title_short | The Characteristic of the Minimal Ideals and the Minimal Generalized Ideals in Rings |
| title_sort | characteristic of the minimal ideals and the minimal generalized ideals in rings |
| url | http://dx.doi.org/10.1155/2023/6478767 |
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