Akira Ooishi
Abstract
In this note, using the notion of various genera of local rings, we prove the following theorem:If (R,m) is an elliptic surface singularity, then the graded ring is Cohen-Macaulay for any integrally closed m-primary ideal I, and m nis integrally closed for all n whenever emb (R) ≤ e( R ).
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In this note, using the notion of various genera of local rings, we prove the following theorem:If (R,m) is an elliptic surface singularity, then the graded ring is Cohen-Macaulay for any integrally closed m-primary ideal I, and m nis integrally closed for all n whenever emb (R) ≤ e( R ).
Key concepts: Integrally closed, Local ring, Mathematics, Ideal (ethics), Singularity, Pure mathematics, Maximal ideal, Ring (chemistry)