The t-Class Group of a Semigroup Ring

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: semigroup ring (t-)class group Mori domain pseudo-Dedekind domain PVMD
• 年，卷（期）: 2001,（4）
• 页码范围: 419-426
• 页数: 8页
• 分类号: O1
• 语种: 英文

摘要

Let S be an integrally closed torsion-free grading monoid with quotient group G, and R an integral domain with quotient field K. We show that if each non-zero element of G is of type (0, 0,... ), then every t-ideal J of K[S] is of the form J ＝ Hk[I] for some h ∈ K[G] and t-ideal I of S. Using this, we also show that if the semigroup ring R[S] is a PVMD and each non-zero element of G is of type (0,0,...), then Clt(R[S]) ≌ Clt(R) Clt(S).