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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 ...
Diagram of ring theory showing circles of acquaintance and direction of travel for comfort and "dumping" Ring theory is a concept or paradigm in psychology that recommends a strategy for dealing with the stress a person may feel when someone they encounter, know or love is undergoing crisis. [ 1 ]
Oral literature is especially rich in chiastic structure, possibly as an aid to memorization and oral performance. In Homer's Iliad and Odyssey, for instance, Cedric Whitman finds chiastic patterns "of the most amazing virtuosity" that simultaneously perform both aesthetic and mnemonic functions, permitting the oral poet easily to recall the basic structure of the composition during ...
The study of rings originated from the theory of polynomial rings and the theory of algebraic integers. [11] In 1871, Richard Dedekind defined the concept of the ring of integers of a number field. [12] In this context, he introduced the terms "ideal" (inspired by Ernst Kummer's notion of ideal number) and "module" and studied their properties ...
The principal ideal theorem and the generalization, the height theorem, both follow from the fundamental theorem of dimension theory in commutative algebra (see also below for the direct proofs). Bourbaki's Commutative Algebra gives a direct proof. Kaplansky's Commutative Rings includes a proof due to David Rees.
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.
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 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 .