An Introduction to i-Commutative Rings

Muhammad Saad (), Usama A. Aburawash, Ahmed M. A. El-Sayed and Nour Nabil
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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

Mathematics, 2025, vol. 13, issue 2, 1-14

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.

Keywords: i-commutative; i-reversible; idempotent; triangular matrix rings; Morita context (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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