%0 Journal Article
%T σ-sporadic prime ideals and superficial elements
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Kamano, D.
%A Essan, K.A.
%A Abdoulaye, A.
%A Akeke, E.D.
%D 2017
%\ 12/01/2017
%V 5
%N 2
%P 35-45
%! σ-sporadic prime ideals and superficial elements
%K Noetherian ring
%K Filtration
%K semi-prime operation
%K associated prime ideals
%K superficial elements
%R 10.22124/jart.2017.2714
%X Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $\sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $\sigma(I^n)$, which denoted by $Ass(A/\sigma(I^n))$, stabilize to $A_{\sigma}(I)$. We give some properties of the sets $S^{\sigma}_{n}(I)=Ass(A/\sigma(I^n))\setminus A_{\sigma}(I)$, with $n$ small, which are the sets of $\sigma$-sporadic prime divisors of $I$.We also give some relationships between $\sigma(f_I)$-superficial elements and asymptotic prime $\sigma$-divisors, where $\sigma (f_I)$ is the $\sigma$-closure of the $I$-adic filtration $f_I=(I^n)_{n\in\mathbb{N}}$.
%U https://jart.guilan.ac.ir/article_2714_3bb28c732e69e2ea353a223c92597da3.pdf