Let A be a commutative ring and I an ideal of A. The amalgamated duplication of A along I,
denoted by A ⋈ IA⋈ I, is the special subring of A * AA× A defined by A ⋈ I:= π AI π={(a, a+ i) …

Let be a ring graded by an arbitrary grading abelian group Γ. We say that R is a uniformly
graded-coherent ring if there is a map ϕ: ℕ→ ℕ such that for every n∈ ℕ, and any nonzero …

In this paper, we introduce a new class of ring called regular S-Noetherian ring, which is a
weak version of S-Noetherian ring property. Any S-Noetherian ring is naturally a regular S …

In this paper, we say a ring $ R $ is Nil $ _ {\ast} $-Noetherian provided that any nil ideal is
finitely generated. First, we show that the Hilbert basis theorem holds for Nil $ _ {\ast} …

Medical image segmentation is an important means to assist doctors in making accurate
diagnoses. However, medical images are often subject to noise interference, and the high …

Let R be a commutative ring with nonzero identity and S⊆ R be a multiplicatively closed
subset of R. In this paper, we introduce and study S-Nil∗-coherent rings which are a …

Let R=⊕ α∈ Γ Rα be a ring graded by an arbitrary grading abelian group Γ. We say that R is
a weakly uniformly graded-coherent ring if there is a map ϕ: N→ N such that for every n∈ N …

In this paper, we introduce a weak version of Noetherianity that we call regular Noetherian
property. A ring is called regular Noetherian, if every regular ideal is finitely generated. We …

Several authors have introduced various types of coherent-like rings and proved analogous
results on these rings. It appears that all these relative coherent rings and all the used …