| 引用本文: | 罗玉祥1,陈 刚2,任 伟1?.可分 Frobenius 扩张下的 Gorenstein 余挠维数(J/M/D/N,J:杂志，M：书，D：论文，N：报纸).期刊名称,2024，41（2）：115-120 |
| CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435 |
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| 摘要: |
| 针对环变化下的 Gorenstein 同调性质,提出模的 Gorenstein 余挠性质及相应维数在环的可分 Frobenius 扩张
下的保持性质。 首先证明对可分 Frobenius 扩张 R→S,S-模 M 是 Gorenstein 余挠模当且仅当 M 是 Gorenstein 余挠的
R-模,从而可得模的 Gorenstein 余挠维数沿着该环扩张保持不变; 作为应用,证明了若该环扩张是可裂的,则环的
整体 Gorenstein 余挠维数也保持不变;此外,讨论了群环上的 Gorenstein 余挠维数,进一步验证 Gorenstein 余挠维数
在环的可分 Frobenius 扩张下的不变性。 |
| 关键词: Gorenstein 余挠 Frobenius 扩张 可分扩张 群环 |
| DOI： |
| 分类号: |
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| Gorenstein Cotorsion Dimension under Separable Frobenius Extensions |
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LUO Yuxiang1,CHEN Gang2, REN Wei1?
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1. School of Mathematical Sciences Chongqing Normal University Chongqing 401331 China
2. No. 3 Middle School of Chongqing University Town Chongqing 401331 China
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| Abstract: |
| For the Gorenstein homological properties under changes of rings the Gorenstein cotorsion property of modules
and the preserving property of the corresponding dimension under a separable Frobenius extension of the ring were
proposed. It was first proved that for a separable Frobenius extension R→S the S-module M was a Gorenstein cotorsion
module if and only if M was an R-module of a Gorenstein cotorsion module and thus the Gorenstein cotorsion dimension of
modules remain invariant along such ring extension. As an application it was shown that if this ring extension was
splittable the overall Gorenstein cotorsion dimension of the ring remained invariant as well. In addition the Gorenstein
cotorsion dimensions over group rings were discussed and the invariance of the Gorenstein cotorsion dimensions under the
separable Frobenius extensions was further verified |
| Key words: Gorenstein cotorsion Frobenius extension separable extension group ring |
