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Generalization of the S -Noetherian concept

Abdelamir Dabbabi, Ali Benhissi (2023)

Archivum Mathematicum

Let A be a commutative ring and 𝒮 a multiplicative system of ideals. We say that A is 𝒮 -Noetherian, if for each ideal Q of A , there exist I ∈ 𝒮 and a finitely generated ideal F ⊆ Q such that I Q ⊆ F . In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

Let R and S be commutative rings with unity, f : R → S a ring homomorphism and J an ideal of S . Then the subring R ⋈ f J : = { ( a , f ( a ) + j ) ∣ a ∈ R and j ∈ J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R ⋈ f J is a (generalized) filter ring.

Generalized tilting modules over ring extension

Zhen Zhang (2019)

Czechoslovak Mathematical Journal

Let Γ be a ring extension of R . We show the left Γ -module U = Γ ⊗ R C with the endmorphism ring End Γ U = Δ is a generalized tilting module when R C is a generalized tilting module under some conditions.

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