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( δ , 2 ) -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

Let R be a commutative ring with nonzero identity, let ℐ ( ℛ ) be the set of all ideals of R and δ : ℐ ( ℛ ) → ℐ ( ℛ ) an expansion of ideals of R defined by I ↦ δ ( I ) . We introduce the concept of ( δ , 2 ) -primary ideals in commutative rings. A proper ideal I of R is called a ( δ , 2 ) -primary ideal if whenever a , b ∈ R and a b ∈ I , then a 2 ∈ I or b 2 ∈ δ ( I ) . Our purpose is to extend the concept of 2 -ideals to ( δ , 2 ) -primary ideals of commutative rings. Then we investigate the basic properties of ( δ , 2 ) -primary ideals and also discuss the relations among ( δ , 2 ) -primary, δ -primary and...

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