具有radical立方零的局部环上的无环性
Acyclicity over local rings with radical cube zero
摘要：
本文研究了交换Noether局部环$(R,m)$与$m^3=0$上自由模生成的无限无圈复形.得到了无圈复形模秩增长的结论，并给出了全无圈的新的充分条件。结果也得到了环的结构，承认无环复合物，这种结构的一部分是由每个环$R$，承认一个非自由的生成非零模块$M$与$Ext^n(M,R)=0$的几个$n>0$。
英文摘要：
This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring $(R,m)$ with $m^3=0$. Conclusive results are obtained on the growth of the ranks of the modules in acyclic complexes, and new sufficient conditions are given for total acyclicity. Results are also obtained on the structure of rings that admit acyclic complexes; part of this structure is exhibited by every ring $R$ that admits a non-free finitely generated non-zero module $M$ with $Ext^n(M,R)=0$ for a few $n>0$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
