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An Introduction to i-Commutative Rings

Author

Listed:
  • Muhammad Saad

    (Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt)

  • Usama A. Aburawash

    (Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt)

  • Ahmed M. A. El-Sayed

    (Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt)

  • Nour Nabil

    (Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt)

Abstract

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 a b + c d is a nontrivial idempotent, then b a + d c 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.

Suggested Citation

  • Muhammad Saad & Usama A. Aburawash & Ahmed M. A. El-Sayed & Nour Nabil, 2025. "An Introduction to i-Commutative Rings," Mathematics, MDPI, vol. 13(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:253-:d:1566605
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