Maximal non-ϕ-pseudo-valuation rings
The notion of maximal non-ϕ-pseudo-valuation ring is introduced which generalizes the
concept of maximal non-pseudo-valuation domain. The equivalence of maximal non-ϕ-PVR
and maximal non-local ring is established under some conditions. The concept of maximal
non-PVR is also introduced and it is shown that a maximal non-PVR is either a ϕ-PVR or a
maximal non-ϕ-PVR. Examples are also given to show that all the introduced concepts are
independent of each other, in general.
concept of maximal non-pseudo-valuation domain. The equivalence of maximal non-ϕ-PVR
and maximal non-local ring is established under some conditions. The concept of maximal
non-PVR is also introduced and it is shown that a maximal non-PVR is either a ϕ-PVR or a
maximal non-ϕ-PVR. Examples are also given to show that all the introduced concepts are
independent of each other, in general.
The notion of maximal non--pseudo-valuation ring is introduced which generalizes the concept of maximal non-pseudo-valuation domain. The equivalence of maximal non--PVR and maximal non-local ring is established under some conditions. The concept of maximal non-PVR is also introduced and it is shown that a maximal non-PVR is either a -PVR or a maximal non--PVR. Examples are also given to show that all the introduced concepts are independent of each other, in general.
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