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Approximations and endomorphism algebras of modules.


Approximations and endomorphism en·do·mor·phism  
1. A change within an intrusive igneous rock caused by the assimilation of portions of the surrounding rock.

2. A homomorphism that maps a mathematical system into itself.
 algebras of modules.

Goebel, Ruediger and Jan Trlifaj.

Walter de Gruyter


640 pages



De Gruyter expositions in mathematics; 41


This mathematical monographs brings together the use of realization theorems This is a list of theorems, by Wikipedia page. See also
  • list of fundamental theorems
  • list of lemmas
  • list of conjectures
  • list of inequalities
  • list of mathematical proofs
  • list of misnamed theorems
  • Existence theorem
 related to the non-classification theory of the category of Mod-R of arbitrary modules over a general associative as·so·ci·a·tive  
1. Of, characterized by, resulting from, or causing association.

2. Mathematics Independent of the grouping of elements.
 unital ring R combined with the approximation theory In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterising the errors introduced thereby. Note that what is meant by best and simpler will depend on the application.  of modules, which has been developed in order to select suitable subcategories C that allow classification, and then approximate arbitrary modules by the ones from C. The authors first develop the approximation theory of modules, together with recent applications (including to infinite- dimensional tilting theory) and then develop prediction principles as tools to obtain the realization theorems. The intended audience includes graduate students interested in algebra algebra, branch of mathematics concerned with operations on sets of numbers or other elements that are often represented by symbols. Algebra is a generalization of arithmetic and gains much of its power from dealing symbolically with elements and operations (such as , as well as experts in module and representation theory.

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Date:Dec 1, 2006
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