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- Title
SOME PROPERTIES OF MONOMIAL IDEALS ON REGULAR SEQUENCES IN A NOETHERIAN RING.
- Authors
Naghipour, Reza; Mollamahmoudi, Simin
- Abstract
In this paper, we continue the study of monomial ideals with respect to a regular sequence on a commutative Noetherian ring R. Let x := x1 ... xd be a regular R-sequence contained in the Jacobson radical of R. We first show that each monomial ideal a of R with respect to x has a unique decomposition as an irredundant finite intersection of ideals of the ... are positive integers. As a consequence, it follows that a is an irreducible ideal if and only if it is a generalized-parameter ideal. In addition, it is shown that if xR is a prime ideal, then the radical of a and the symbolic powers of a are monomials. Finally, we prove that if a is a square-free monomial ideal such that ... for all integers k > 1, then a is normal and a(k) = ak, where a(k) denotes the kth symbolic power of a.
- Subjects
NOETHERIAN rings; JACOBSON radical; PRIME ideals; POWER (Social sciences); POLYNOMIAL rings; INTEGERS; COMMUTATIVE rings; REGULAR graphs
- Publication
Palestine Journal of Mathematics, 2021, Vol 10, Issue 2, p802
- ISSN
2219-5688
- Publication type
Article