… ideals and semi n-ideals, we define a proper ideal I of a ring R to be a semi r-ideal if
whenever a ∈ R such that a2 ∈ I and AnnR(a) = 0, then a ∈ I. It is clear that the class of semi r-…

… Let R be a commutative ring with identity and N(R) and J (R) denote the nilradical and the …
study J-ideals as a new generalization of n-ideals in commutative rings. A proper ideal I of R is …

Let R be a commutative ring with nonzero identity. In this paper, we introduce and investigate
a generalization of (2, J)-ideals. Let φ: I (R)→ I (R)∪{∅} be a function where I (R) is the set …

… In this note, we extend these notions to non-commutative rings … Hence for commutative rings
the notions β, L and N-ideals … (2) If R is a semi-prime ring which is not a prime ring, then R …

We provide some characterizations of completely prime (completely semiprime) and 3-prime
(3-semiprime) N-groups. The relationship between a 3-prime (completely prime) N-ideal P …

… , n-ideals and J-ideals of a commutative ring with identity to multiplicative lattices. In fact,
we prove that an ideal I of a commutative ring … (semi-ideal) I of a lattice L is a proper ideal (semi-…

Background: This study gives a new generalization to Ids called 𝑃𝑛-Id. If for all 𝑎, 𝑏∈ 𝑅
with 𝑎𝑏∈ 𝐼 and 𝑎∉√ 0 then 𝑏∈√ 𝐼, and a proper Id P of 𝑅 is known as a 𝑃𝑛− Id. It …

… and Mott characterize commutative rings (even without an identity) over which every semi-…
in the context of commutative rings with identity, we deduce immediately the following result. …

… n-ideals in commutative rings In 2017 Tekir, Koc and Oral introduced the notion of n-ideals
for a commutative ring R … notion of n-ideals for a commutative ring R with identity element: Let …

… notions to non-commutative rings and show that … a commutative ring as new generalization
of J -ideals. In this note, we extend the notion of a weakly J -ideal to non-commutative rings …