section_path: Contributions to mathematics and physics/Third epoch (1927–1935)/Hypercomplex numbers and representation theory
section_name: Hypercomplex numbers and representation theory
paragraph_text: Hypercomplex numbers and representation theory
  
  Much work on hypercomplex numbers and group representations was carried out in the nineteenth and early twentieth centuries, but remained disparate. Noether united these earlier results and gave the first general representation theory of groups and algebras. This single work by Noether was said to have ushered in a new period in modern algebra and to have been of fundamental importance for its development.
  
  Briefly, Noether subsumed the structure theory of associative algebras and the representation theory of groups into a single arithmetic theory of modules and ideals in rings satisfying ascending chain conditions.