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- Title
Some Results on the Associated Primes of Monomial Ideals.
- Authors
Khashyarmanesh, K.; Nasernejad, M.
- Abstract
Let R = K[x1, . . ., xn] be the polynomial ring, where K is a field and x1, . . ., xn are indeterminates. Let ... = {p1, . . ., pm} and B = {p′1, . . ., p′t} be two arbitrary sets of monomial prime ideals of R such that the elements of A ∪B are minimal with respect to inclusion. We show that there exist unique square-free monomial ideals I and J of R with the following properties: (i) AssR(R/I) = A, AssR(R/J) = B; and, (ii) I ⊆ J and AssR(J/I) = A\B. In the sequel, we investigate the associated prime ideals of monomial ideals under squeezing. Finally, we state two recursive formulas for associated prime ideals.
- Subjects
POLYNOMIAL rings; PRIME numbers; EXISTENCE theorems; SET theory; MATHEMATICAL models
- Publication
Southeast Asian Bulletin of Mathematics, 2015, Vol 39, Issue 3, p439
- ISSN
0129-2021
- Publication type
Article