Let $\bar{I}$ denote the integral closure of an ideal in a Noetherian ring $R$. The main result of this paper asserts that $R$ is locally quasi-unmixed if and only if, the topologies defined by $\overline{I^n}$ and $I^{\langle n\rangle}$, $\ n\geq 1$, are equivalent. In addition, some results about the behavior of linearly equivalent topologies of ideals under various ring homomorphisms are included.
associated primes linearly equivalent topologies integral closure locally quasi-unmixed ring Rees ring
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 8 Ağustos 2019 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 48 Sayı: 4 |