TY - JOUR
ID - 1998
TI - I-prime ideals
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Akray, I.
AD - Soran University
Y1 - 2016
PY - 2016
VL - 4
IS - 2
SP - 41
EP - 47
KW - prime ideal
KW - weakly prime ideal
KW - almost prime ideal
KW - radical of the ideal
DO -
N2 - In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties. Moreover, we give conditions under which $I$-prime ideals becomes prime or weakly prime and we construct the view of $I$-prime ideal in decomposite rings.
UR - https://jart.guilan.ac.ir/article_1998.html
L1 - https://jart.guilan.ac.ir/article_1998_805b509c5392f49a246ca25b4fb110a2.pdf
ER -