Let R=⊕ α∈ Γ R α be an integral domain graded by an arbitrary torsionless grading monoid
Γ. We say that R is a graded Prüfer domain if every nonzero finitely generated …

Let Γ be a nonzero commutative cancellative monoid (written additively), R=⊕ α∈ Γ R α be
a Γ-graded integral domain with R α≠{0} for all α∈ Γ, and H be the set of nonzero …

Let Γ be a torsionless commutative cancellative monoid, R=⊕ α∈ Γ R α be a Γ-graded
integral domain, and H be the set of nonzero homogeneous elements of R. In this paper, we …

Let $\Gamma $ be a torsionless commutative cancellative monoid and $ R=\bigoplus_
{\alpha\in\Gamma} R_ {\alpha} $ be a $\Gamma $-graded integral domain. In this paper, we …

Let Γ be a torsionless commutative cancellative monoid and R=⊕ α∈ Γ R α be a Γ-graded
integral domain. In this paper, we provide necessary and sufficient conditions for R to be a …

Perinormal and globally perinormal domains were first introduced by Epstein and Shapiro in
[ES16]. They showed that perinormality is close to normality which one can think of as being …

Let D be an integral domain with quotient field K, X be an indeterminate over D, K [X] be the
polynomial ring over K, and $ R=\{f {\in} K [X]{\mid} f (0){\in} D\} $; so R is a subring of K [X] …

Let R= ⨁ _ α ∈ Γ R_ α R=⨁ α∈ Γ R α be a graded integral domain and ⋆⋆ be a semistar
operation on R. For a ∈ R a∈ R, denote by C (a) the ideal of R generated by homogeneous …

Let $ R=\bigoplus_ {\alpha\in\Gamma} R_ {\alpha} $ be an integral domain graded by an
arbitrary torsionless grading monoid $\Gamma $, $\bar {R} $ be the integral closure of $ R …

Let R=⊕ α∈ Γ Rα be a graded integral domain, H be the set of nonzero homogeneous
elements of R, and⋆ be a semistar operation on R. The purpose of this paper is to study the …