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Abstract
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Let R denote a commutative noetherian ring, and let x :=x1,..., xd be an R-regular sequence. Suppose that a denotes a monomial ideal with respect to x. The first purpose of this article is to show that a is irreducible if and only if a is a generalized-parametric ideal. Next, it is shown that, for any integer n>=1, (x_1,...,x_d)^n=\cap P(f), where the intersection (irredundant) is taken over all monomials f=x_1^e_1...x_d^e_d such that deg(f) = n-1 and P(f) := (x_1^e_1+1...x_d^e_d+1 ). The second main result of this paper shows that if q := (x) is a prime ideal of R which is contained in the Jacobson radical of R and R is q-adically complete, then a is a parameter ideal if and only if a is a monomial irreducible ideal and Rad(a) = q. In addition, if a is generated by monomials m_1,...,m_r; then Rad(a), the radical of a, is also monomial and Rad(a) = (w_1,...,w_r), where w_i=rad(m_i) for all i = 1,...,r..
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