## 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:

**Abstract Algebra**

... upon physics, among mathematicians she is best remembered for her seminal contributions to

**abstract algebra**... says in his Introduction to Noether's Collected Papers, The development of

**abstract algebra**, which is one of the most distinctive innovations of twentieth ... Noether's groundbreaking work in

**algebra**began in 1920 ...

**Abstract Algebra**

... The ability to do

**algebra**is a skill cultivated in mathematics education ... Eventually mathematics was concerned completely with

**abstract**polynomials, complex numbers, hypercomplex numbers and other concepts ... mathematics or mathematical physics, and the field of mathematics expanded to include

**abstract algebra**...

**Abstract Algebra**- Applications

... Because of its generality,

**abstract algebra**is used in many fields of mathematics and science ... describe those symmetries 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 theory is equal to dimension of the Lie ...

...

**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**" ...

... and the notation F1 are only suggestive, as there is no field with one element in classical

**abstract algebra**... the traditional building blocks for

**abstract algebra**, with other, more flexible objects ... Instead, most proposed theories of F1 replace

**abstract algebra**entirely ...

### Famous quotes containing the words algebra and/or abstract:

“Poetry has become the higher *algebra* of metaphors.”

—José Ortega Y Gasset (1883–1955)

“Somebody once said that I am incapable of drawing a man, but that I draw *abstract* things like despair, disillusion, despondency, sorrow, lapse of memory, exile, and that these things are sometimes in a shape that might be called Man or Woman.”

—James Thurber (1894–1961)