The main purpose of this article is to explain homological technique in commutative algebra by studying the notion of depth by means of Ext and by applying it to a problem of linear equations, namely the Buchsbaum-Eisenbud criterion of exactness of finite free complexes. Our second purpose is ...
An Introduction to Homological Algebra Rotman An Introduction to Homological Algebra by Weibel Methods of Homological Algebra by SergeiI. Gelfand, Yuri Manin 我首先要说一句,上面的五本书,前两本书我仅仅是翻过,没有认真拜读过,因此对它们的评价可能会有失偏颇,尽管这些评价是来自其他书籍作者只言片语的...
As commutative algebra took on new life with the infusion of homological methods , he turned his interest once more in this direction, always trying to see past the formalism into "what was really going on". 作为交换代数了新的生活注入同源的方法, 他把他的兴趣再一次在这个方向发展,总是试图...
Homological Algebra has grown in the nearly three decades since the rst e- tion of this book appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to Homological Algebra, 1994, and Gelfand– Manin, Methods of Homological Algebra, 2003. In their Foreword, Gelfan...
which is the main result of [2] obtained by different methods. Since the localization functor L:D(C∗(GX,Fp))→D(C∗(GX+p,Fp))L:D(C*(GX,𝔽p))→D(C*(GXp+,𝔽p)) is always smashing, it makes sense to ask whether it is finite, i.e. whether ...
1 Tor for abelian groups This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give two examples to motivate the definition of the groups Tor(A,B), from the universal coefficient th...
"[...] in the reviewer’s opinion it is an elegant introduction to homological methods towards applications in ring theory."Zentralblatt für Mathematik Topics Algebra and Number Theory Mathematics eBook Published:October 27, 2011 ISBN:9783110215212 ...
When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occu...
Homological and Commutative Algebra Our second purpose is to look at concrete categories and see what the general methods of homological algebra yield in particular cases. More precisely, we shall look at the category of finitely generated modules over a local ring and, us... D Buchsbaum 被引...
Using methods developed by Franke, we obtain algebraic classification results for modules over certain symmetric ring spectra ($S$-algebras). In particular... Patchkoria,Irakli - 《Algebraic & Geometric Topology》 被引量: 33发表: 2013年 Statistical mechanics of magnetohydrodynamics the spectra of the...