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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/2/253 |
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| Summary: | 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. |
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| ISSN: | 2227-7390 |