On quası n-ideals of commutative rings - ASLANKARAYİĞİT UĞURLU, EMEL (My University, 2022)
Let R be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of n-ideals and the class of (2, n)-ideals. A proper ideal I of R is said to be a quasi n-ideal if root I is an n-ideal of R. Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the n-ideals, the quasi primary ideals, the (2, n)-ideals and the pr-ideals. Moreover, we use the quasi n-ideals to characterize some kind of rings. Finally, we investigate quasi n-ideals under various contexts of constructions such as direct product, power series, idealization, and amalgamation of a ring along an ideal.
Keywords: Matematik; Temel Bilimler (SCI); MATHEMATICS; Natural Sciences (SCI); Analiz; Cebir ve Sayı Teorisi; Matematik (çeşitli); Genel Matematik; Fizik Bilimleri; Analysis; Algebra and Number Theory; Mathematics (miscellaneous); General Mathematics; Physical Sciences; n-ideal; quasi n-ideal; (2, n)-ideal; 13A15; 13A18; n-ideal; quasi n-ideal; (2; n)-ideal