@article {
author = {Kamano, D. and Essan, K.A. and Abdoulaye, A. and Akeke, E.D.},
title = {σ-sporadic prime ideals and superficial elements},
journal = {Journal of Algebra and Related Topics},
volume = {5},
number = {2},
pages = {35-45},
year = {2017},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {10.22124/jart.2017.2714},
abstract = {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 $f_I=(I^n)_{n\in\mathbb{N}}$.},
keywords = {Noetherian ring,Filtration,semi-prime operation,associated prime ideals,superficial elements},
url = {https://jart.guilan.ac.ir/article_2714.html},
eprint = {https://jart.guilan.ac.ir/article_2714_3bb28c732e69e2ea353a223c92597da3.pdf}
}