abstract algebra

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  • He worked mainly in abstract algebra, but made important contributions to number theory.
  • The 19th century saw the beginning of a great deal of abstract algebra.
  • Almost all structures in abstract algebra are special cases of groups.
  • He put a lot of effort into building up the Mainz group theory and abstract algebra research groups.
  • He is known for his research and textbooks in group theory and abstract algebra.
  • In abstract algebra, field extensions are the main object of study in field theory.
  • Directed sets also give rise to direct limits in abstract algebra and (more generally) category theory.
  • His research interests include abstract algebra, number theory, group schemes, and the history of mathematics.
  • He wrote a number of influential research papers in abstract algebra.
  • His mathematical work was in algebraic number theory and abstract algebra, especially group theory.
  • In abstract algebra, it can be shown that any complete ordered field is isomorphic to the real numbers.
  • Two of the most basic objects in abstract algebra are groups and rings.
  • Both rules are wholly familiar from school mathematics and from abstract algebra generally.
  • Abstract algebra emerged around the start of the 20th century, under the name modern algebra.
  • An operation d with these two properties is known in abstract algebra as a derivation.
  • He become known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra.
  • Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
  • Because of its generality, abstract algebra is used in many fields of mathematics and science.
  • Theorems of abstract algebra are powerful because they are general; they govern many systems.
  • The term modern algebra has also been used to denote abstract algebra.
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