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 Buchsb
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...
Two excellent books on homological algebra are the "Homological algebra" by Cartan and Eilenberg, and "An introduction to homological algebra" by C. Weibel. Reading: Section Exercises: 2 properties of Tor We check the basis properties of Tor(A,B) for abelian groups: (1) It is well defined...
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 ...
Cambridge Studies in Advanced Mathematics(共87册), 这套丛书还有 《An Introduction to Invariants and Moduli》《Multidimensional Real Analysis II》《Additive Combinatorics》《Cohomological Methods in Transformation Groups》《Geometry of Sets and Measures in Euclidean Spaces》 等。
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 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...
The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological...
consider the behavior of this construction in relation to the usual concepts of algebra: homomorphisms, submodules, quotient modules, etc. To facilitate the discussion of this behavior we adopt diagrammatic methods. A sequence of A-modules and A-homomorphisms ...
929 accesses 1 citation explore all metrics abstract we study translationally invariant pauli stabilizer codes with qudits of arbitrary, not necessarily uniform, dimensions. using homological methods, we define a series of invariants called charge modules. we describe their properties and physical meaning...