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Download as PDF; Printable version; ... ring theory is the study of ... T. Y. (2003), Exercises in Classical Ring Theory, Problem Books in Mathematics (Second ed ...
This work is systematized in their monograph Almost ring theory. [1] More foundational material was developed after the first book, and especially an extended theory of perfectoid rings and perfectoid spaces which generalizes the recent work of Peter Scholze. These aspects were recapitulated in the book "Foundations for Almost Ring Theory". [2]
Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over ), simplicial commutative rings or -ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g., Tor) of the structure sheaf.
In commutative and homological algebra, the grade of a finitely generated module over a Noetherian ring is a cohomological invariant defined by vanishing of Ext-modules [1] = = {: (,)}.
In mathematics, Goldie's theorem is a basic structural result in ring theory, proved by Alfred Goldie during the 1950s. What is now termed a right Goldie ring is a ring R that has finite uniform dimension (="finite rank") as a right module over itself, and satisfies the ascending chain condition on right annihilators of subsets of R.
In mathematics, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers The main article for this category is Ring theory .
The following equivalent definitions of a left perfect ring R are found in Anderson and Fuller: [2]. Every left R-module has a projective cover.; R/J(R) is semisimple and J(R) is left T-nilpotent (that is, for every infinite sequence of elements of J(R) there is an n such that the product of first n terms are zero), where J(R) is the Jacobson radical of R.
Spectrum (ring theory) From Wikipedia, the free encyclopedia ... Print/export. Download as PDF; Printable version; Languages. Add links.