Isomorphism theorems

In the mathematical field of abstract algebra, the isomorphism theorems consist of three (or sometimes four) theorems describing the structure of homomorphisms of many different types of algebraic structures. These theorems are generalizations of some of the fundamental ideas from linear algebra, notably the rank–nullity theorem, and are encountered frequently in group theory. The isomorphism theorems are also fundamental in the field of K-theory, and arise in ostensibly non-algebraic situations such as functional analysis (in particular the analysis of Fredholm operators.)