an irredundant primary decomposition is: and the associated primes are obviously the idea is

to first write your ideal as an ideal generated by some monomials. in here we have: this is equal to the intersection of all ideals generated by

7 monomials, each chosen from one of the generators of many of these ideals are subsets of some others and so we just delete them. it is important to know that a monomial ideal in

a polynomial ring where is a field, is primary if and only if it's in the form where are monomials in for

example in the ideal is primary but is not primary.