Let $R$ be a commutative ring with identity. A proper ideal $P$ of $R$ is a<n> $(n-1,n)$-$\Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,\ldots,a_n\in R$, $a_1\cdots a_n\in P\backslash P^m$ ($a_1\cdots a_n\in P\backslash \{0\}$) implies $a_1\cdots a_{i-1}a_{i+1}\cdots a_n\in P$, for some $i\in\{1,\ldots,n\}$; ($m,n\geq 2$). In this paper several results concerning $(n-1,n)$-$\Phi_m$-prime and $(n-1,n)$-weakly prime ideals are proved. We show that in a Noetherian domain a $\Phi_m$-prime ideal is primary and we show that in some well known rings $(n-1,n)$-$\Phi_m$-prime ideals and $(n-1,n)$-prime ideals coincide.
Ebrahimpour, M. (2014). On generalisations of almost prime and weakly prime ideals. Bulletin of the Iranian Mathematical Society, 40(2), 531–540.
MLA
Ebrahimpour, M. "On generalisations of almost prime and weakly prime ideals", Bulletin of the Iranian Mathematical Society, 40, 2, 2014, 531–540.
HARVARD
Ebrahimpour, M. (2014). 'On generalisations of almost prime and weakly prime ideals', Bulletin of the Iranian Mathematical Society, 40(2), pp. 531–540.
CHICAGO
Ebrahimpour, M., "On generalisations of almost prime and weakly prime ideals." Bulletin of the Iranian Mathematical Society, 40 2 (2014): 531–540,
VANCOUVER
Ebrahimpour M. On generalisations of almost prime and weakly prime ideals. BIMS. 2014;40(2):531–540.
