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On n-semiprimary ideals and n-pseudo valuation domains
Anderson, David F. Badawi, Ayman
Anderson, David F.
Badawi, Ayman
Date
2020-08-14
Authors
Advisor
Type
Article
Peer-Reviewed
Postprint
Peer-Reviewed
Postprint
Degree
Citations
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Description
Let R be a commutative ring with 1 ≠0 and n a positive integer. A proper ideal I of R is an n-semiprimary ideal of R if whenever x^n y^n ∈ I for x, y ∈ R, then x^n ∈ I or y^n ∈ I. Let R be an integral domain with quotient field K. A proper ideal I of R is an n-powerful ideal of R if whenever x^n y^n ∈ I for x, y ∈ K, then x^n ∈ R or y^n ∈ R; and I is an n-powerful semiprimary ideal of R if whenever x^n y^n ∈ I for x, y ∈ K, then x^n ∈ I or y^n ∈ I. If every prime ideal of R is an n-powerful semiprimary ideal of R, then R is an n-pseudo-valuation domain (n-PVD). In this paper, we study the above concepts and relate them to several generalizations of pseudo-valuation domains.