Abstract
In this work we introduce the notion of P-Ikeda-Nakayama rings (\P-IN-rings") which is in some way a generalization of the notion of IkedaNakayama rings (\IN-rings"). Then, we study the transfer of this property to trivial ring extension, localization, homomorphic image and to the direct product.
Highlights
That we can respond to this question, we are in need of the results of the following theorem
AnnR(I) ⊆ M ∝ E
We examine the context of trivial ring extensions of a domain by its quotient field
Summary
Let (A, M ) be a local domain with maximal ideal M , E be an A-module such that M E = 0, and R := A ∝ E be the trivial ring extension of A by E. AnnR(I) ⊆ M ∝ E (since R is a local ring with maximal ideal M ∝ E and e = 0).
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