同调代数 meaning in English
homological algebra
Examples
- Homological algebra plays such an important part in modern developments .
同调代数在现代发展中起了如此重要的作用。 - Morita duality is an important concept in module theory
Morita对偶是模论与同调代数理论中又一重要的概念。 - In this paper , the stability and multiplicity of closed geodesics are considered on some compact simply connected manifolds with the eohomology algebra td , n ( x ) of truncated polynomial algebra
本文研究一类单连通紧流形上的闭测地线的多重性与稳定性,这类流形具有截断多项式代数作为其同调代数 - Since the k - gorenstein property of ring r x m is an important aspect in the research field , in the first chapter , we have got an equivalent condition for r m as a k - gorenstein ring by study the injective resolution of ring r m . the dimensions of rings is one of the most important parts in homological theory
在第一章，我们通过对r ( ? ) m内射分解的考察得到了r ( ? ) m成为k - gorenstein环的一个充分必要条件：维数的研究是同调理论中的核心部分，伴随同调理论的形成，它便一直成为同调代数中研究的焦点。 - Using universal property , we can define general ( pre ) cover and ( pre ) envelope , such as gorenstein injective ( projective or flat ) ( pre ) cover and ( pre ) envelope , 5 - torsion free ( pre ) cover etc . in a word , problems on ( pre ) over and ( pre ) envelope have aroused considerable debate in the academic circle , which embodies flexible use of tools of homological algebra in studying categories of rings and modules
而且利用泛性我们又可定义更广泛意义上的包、盖问题，例如： gorenstin内射(平坦、投射)包(盖) ， s -无挠预盖，等等。用这类比内射(平坦、投射)更广泛意义上的特殊模又能刻画一些环。总之，包、盖问题是当今非常活跃的研究课题，体现了同调代数在环模范畴研究中灵活运用。