2 papers
math.AC2026
Primary decompositions via exponent matrices
Jacob Miller
In this paper we present a new result that exhibits in a non-recursive fashion a primary decomposition of any monomial ideal. Our result is derived from the classical quotient-sum…
math.AC2026
Associated primes, witnesses, and omega invariants of monomial ideals
Jacob Miller, Mehrdad Nasernejad, Ştefan O. Tohǎneanu
We introduce and study the omega invariant of a proper ideal in a Noetherian commutative ring, defined as the number of associated primes of the ideal. Our main objective is to inv…