Let R be a commutative Noetherian ring. Using the new concept of linkage of ideals over a module, we show that if 𝔞 is an ideal of R which is linked by the ideal I, then cd(𝔞,R) ∈{grade𝔞,cd(𝔞,H𝔠grade𝔞(R)) + grade𝔞}, where 𝔠 :=⋂𝔭∈AssR I−V (𝔞)𝔭. Also, it is shown that for every ideal 𝔟 which is geometrically linked with 𝔞, cd(𝔞,H𝔟grade𝔟(R)) does not depend on 𝔟.

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关于相关理想的上同调维度

让R是一个可交换的诺特环。使用模块上理想链接的新概念，我们证明如果𝔞是一个理想的R这是由理想联系起来的一世， 然后光盘(𝔞,R) ∈{年级𝔞,光盘(𝔞,H𝔠年级𝔞(R)) + 年级𝔞},在哪里𝔠 ：=⋂𝔭∈屁股R 一世-五 (𝔞)𝔭. 此外，它表明对于每个理想𝔟在几何上与𝔞, 光盘(𝔞,H𝔟年级𝔟(R))不依赖于𝔟.