Title of article :
σ-SPORADIC PRIME IDEALS AND SUPERFICIAL ELEMENTS
Author/Authors :
essan, k. a. universite peleforo gon coulibaly - ufr sciences sociales, Korhogo, Côte d Ivoire , abdoulaye, a. universite nangui abrogoua - laboratoire de mathematiques et informatique, Abidjan, Côte d Ivoire , kamano, d. ecole normale superieure - department de sciences et technologie, section mathematiques, Abidjan, Côte d Ivoire , akeke, e.d. universite felix houphouet boigny - ufr de mathematiques et informatique, Abidjan, Côte d Ivoire
Abstract :
Let A be a Noetherian ring, I be an ideal of A and σ 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 σ(I n), which denoted by Ass(A/σ(I n), stabilize to Aσ(I). We give some properties of the sets S σ n (I) = Ass(A/σ(I n)Aσ(I), with n small, which are the sets of σ-sporadic prime divisors of I. We also give some relationships between σ(fI )- superficial elements and asymptotic prime σ-divisors, where σ(fI ) is the σ-closure of the I-adic filtration fI = (I n)n∈N.
Keywords :
Noetherian ring , filtration , semi , prime operation , associated prime ideals , superficial elements
Journal title :
Journal of Algebra and Related Topics
Journal title :
Journal of Algebra and Related Topics
