Concepts

Field (Abstract Algebra)

Citation Formats

General Reference

Mathematics Atlas. "Field (Abstract Algebra)." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/concepts/field-abstract-algebra.

APA Style

Mathematics Atlas. (n.d.). Field (Abstract Algebra). Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/concepts/field-abstract-algebra

BibTeX

@misc{mathematicsatlas-field-abstract-algebra,
  author = {Mathematics Atlas},
  title = {Field (Abstract Algebra)},
  year = {2026},
  url = {https://mathematics.interactiveatlas.org/concepts/field-abstract-algebra},
  note = {Accessed August 30, 2026}
}

A field is an algebraic structure that is closed under the four usual arithmetic operations: a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational numbers do. Heinrich Martin Weber gave the first clear abstract definition of a field in 1893.

Facts

Origin Year

1893 1

Cross-Tradition Connections