University of Guilan Journal of Algebra and Related Topics 2345-3931 5 2 2017 12 01 σ-sporadic prime ideals and superficial elements 35 45 2714 10.22124/jart.2017.2714 EN D. Kamano D\&#039;epartment de Sciences et Technologie, Section Math\&#039;ematiques, Ecole normale sup\&#039;erieure, Abidjan, C\^ote d&#039;Ivoire K.A. Essan UFR sciences sociales, Universit&#039;e P&#039;el&#039;eforo Gon Coulibaly, Korhogo, C^ote d&#039;Ivoire A. Abdoulaye Laboratoire de Math\&#039;ematiques et Informatique, Universit\&#039;e Nangui Abrogoua, Abidjan, C\^ote d&#039;Ivoire E.D. Akeke UFR de Math&#039;ematiques et Informatique, Universit&#039;e F&#039;elix Houphouet Boigny, Abidjan, C^ote d&#039;Ivoire Journal Article 2017 12 03 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<br /> $S^{\sigma}_{n}(I)=Ass(A/\sigma(I^n))\setminus A_{\sigma}(I)$, with $n$ small, which are the sets of $\sigma$-sporadic prime divisors of $I$.<br />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 $f_I=(I^n)_{n\in\mathbb{N}}$. https://jart.guilan.ac.ir/article_2714_3bb28c732e69e2ea353a223c92597da3.pdf