What is abstract algebra?

Abstract Algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called elementary algebra. The distinction is rarely made in more recent writings.

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Some articles on abstract algebra:

History Of Elementary Algebra - Modern Algebra - Abstract Algebra
... The ability to do algebra is a skill cultivated in mathematics education ... was concerned completely with abstract polynomials, complex numbers, hypercomplex numbers and other concepts ... or mathematical physics, and the field of mathematics expanded to include abstract algebra ...
Emmy Noether - Biography - Seminal Work in Abstract Algebra
... among mathematicians she is best remembered for her seminal contributions to abstract algebra ... to Noether's Collected Papers, The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her – in published papers, in lectures ... Noether's groundbreaking work in algebra began in 1920 ...
Algebra
... Algebra is related to mathematics, but for historical reasons, the word "algebra" has three meanings as a bare word, depending on the context ... As a single word, "algebra" can mean Use of letters and symbols to represent values and their relations, especially for solving equations ... This is also called "Elementary algebra" ...
Abstract Algebra - Applications
... Because of its generality, abstract algebra is used in many fields of mathematics and science ... are Lie groups, and the study of Lie groups and Lie algebras reveals much about the physical system for instance, the number of force carriers in a ...
Field With One Element
... as there is no field with one element in classical abstract algebra ... operations, the traditional building blocks for abstract algebra, with other, more flexible objects ... Instead, most proposed theories of F1 replace abstract algebra entirely ...

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