… (Other writers have called this space the space of minimal prime ideals, but since we propose
to discuss the dual topology, it seems preferable to avoid this usage.) The following have …

… Let R be a commutative ring and I an ideal of R. We show that if all the prime ideals minimal
over I are finitely generated, then there are only finitely many prime ideals minimal over I. …

… the minimal primes over ideals of 3×3 permanents of a generic matrix, and show that there
are monomials in the ideal … Thus Q contains the prime ideal generated by xi,j for all i and the d…

… We will now give the definition of a minimal prime ideal and prove some … ideal I ⊂ R. On
top of that, we will give two examples of the minimal prime ideals that contain a given ideal I. …

… non- tri vial ideal. Moreover, we prove that if R has at least three minimal prime ideals, then
AG (… It is shown that, for every reduced ring il, if R has at least three minimal prime ideals, then …

… if P # R and xRy CP G- x EP or y E P, and R is called a prime ring if (0) is prime … a prime
ideal of R, then U = C n P will be a prime ideal of C; we shall say that P belongs to the prime ideal …

… hoops is a union of all minimal prime ideals of hoop. Finally, by using the notions … minimal
prime ideals and maximal ideals of hoop, we introduce two new ideals as p-ideal and m-ideal. …

… said to be prime or p-prime (pa prime ideal of R) if rx ∈ N for r ∈ R and x ∈ M implies that
either x ∈ N or r ∈ p. In this paper we study a new equivalent conditions for a minimal prime …

… S is a prime submodule ideal extension (for short PSI-extension… prime ideal of S every ideal
of S which is a prime Rsubmodule of S. In other words, a subset I of S is called R-prime ideal …

… primes in short intervals to prime ideals of the ring of integers in cyclotomic extensions with
norms belonging to such intervals. The extension is uniform with respect to the degree of the …