On a question about almost prime ideals | Zendy

Esmaeil Rostami | Zendy; Reza Nekooei | Zendy

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On a question about almost prime ideals

Author(s) -

Esmaeil Rostami,

Reza Nekooei

Publication year - 2016

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1507-18

Subject(s) - mathematics , prime (order theory) , noetherian , associated prime , ideal (ethics) , prime ideal , fractional ideal , maximal ideal , domain (mathematical analysis) , discrete mathematics , combinatorics , pure mathematics , algebra over a field , epistemology , philosophy , mathematical analysis

In this paper, by giving an example we answer positively the question \Does there exist a P -primary ideal I in a Noetherian domain R such that PI = I 2 , but I is not almost prime?", asked by S. M. Bhatwadekar and P. K. Sharma. We also investigated conditions under which the answer to the above mentioned question is negative.

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