Limit behavior of the rational powers of monomial ideals

We investigate the rational powers of ideals. find that in case monomial ideals, canonical indexing leads to a characterization yielding symbolic squarefree ideals are indeed themselves. Using connection with techniques, we use splittings show convergence depths and normalized Castelnuovo–Mumford regularities. Stanley for powers, as consequence this, before-now unknown integral closure powers. Additionally, finiteness asymptotic associated primes, lengths local cohomology modules converge hence