On 2-nil Primary Ideals of Commutative Rings

The present article addresses the concept of 2-nil primary ideals in commutative rings, expanding the comprehension of ideal categories such as 2-nil, 2-absorbing and quasi primary ideals. The study explores the characteristics and connections of 2-nil primary ideals, offering a comprehensive framework for understanding their significance in ring theory. The paper presents examples and arguments that illustrate the relationship between 2-nil primary ideals and other well-known classes of ideals, such as prime, primary and n-ideals, while highlighting their differences.Furthermore, we investigate how the $2$-nil primary ideal behaves concerning images and inverse images of homomorphism, quotients, localization, products, and idealizations.