An Introduction to i-Commutative Rings
In this paper, we introduce a new class of rings, called i-commutative rings, by extending the concept of commutative-like rings using idempotent elements. In particular, we study rings with the property that, whenever <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML&quo...
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2025-01-01
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| author | Muhammad Saad Usama A. Aburawash Ahmed M. A. El-Sayed Nour Nabil |
| author_facet | Muhammad Saad Usama A. Aburawash Ahmed M. A. El-Sayed Nour Nabil |
| author_sort | Muhammad Saad |
| collection | DOAJ |
| description | In this paper, we introduce a new class of rings, called i-commutative rings, by extending the concept of commutative-like rings using idempotent elements. In particular, we study rings with the property that, whenever <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>b</mi><mo>+</mo><mi>c</mi><mi>d</mi></mrow></semantics></math></inline-formula> is a nontrivial idempotent, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>c</mi></mrow></semantics></math></inline-formula> is idempotent. We explore the basic properties of these rings and their relations with other rings. Moreover, we provide some examples using matrices and describe the structure of the idempotent elements in these rings. |
| format | Article |
| id | doaj-art-f0e14b31534f4bc080c85359ef937660 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-f0e14b31534f4bc080c85359ef9376602025-01-24T13:39:54ZengMDPI AGMathematics2227-73902025-01-0113225310.3390/math13020253An Introduction to i-Commutative RingsMuhammad Saad0Usama A. Aburawash1Ahmed M. A. El-Sayed2Nour Nabil3Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, EgyptIn this paper, we introduce a new class of rings, called i-commutative rings, by extending the concept of commutative-like rings using idempotent elements. In particular, we study rings with the property that, whenever <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>b</mi><mo>+</mo><mi>c</mi><mi>d</mi></mrow></semantics></math></inline-formula> is a nontrivial idempotent, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mi>a</mi><mo>+</mo><mi>d</mi><mi>c</mi></mrow></semantics></math></inline-formula> is idempotent. We explore the basic properties of these rings and their relations with other rings. Moreover, we provide some examples using matrices and describe the structure of the idempotent elements in these rings.https://www.mdpi.com/2227-7390/13/2/253i-commutativei-reversibleidempotenttriangular matrix ringsMorita context |
| spellingShingle | Muhammad Saad Usama A. Aburawash Ahmed M. A. El-Sayed Nour Nabil An Introduction to i-Commutative Rings Mathematics i-commutative i-reversible idempotent triangular matrix rings Morita context |
| title | An Introduction to i-Commutative Rings |
| title_full | An Introduction to i-Commutative Rings |
| title_fullStr | An Introduction to i-Commutative Rings |
| title_full_unstemmed | An Introduction to i-Commutative Rings |
| title_short | An Introduction to i-Commutative Rings |
| title_sort | introduction to i commutative rings |
| topic | i-commutative i-reversible idempotent triangular matrix rings Morita context |
| url | https://www.mdpi.com/2227-7390/13/2/253 |
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