Abstract algebra its the part of mathematis that studies algebraic structures such as groups, rings or vector spaces. many of these structures where totally defined in the 19th century, and, actually, the study of abstract algebra was motivated by the need for more precission in the mathematical definitions.
In abstract algebra, combined elements by diferent operations are not generally interpreted as numbers, being one of the reasons for why abstract algebra can´t just be considered a simple extension of arithmetics. The study of abstract algebra has allowed to observed with clarity the intrinsic logical statements where all maths and natural sciences are based uppon. Also, along the history, the algebraists discoverd logical structures that while apparently different very often they can be characterized by the same way with a little group of axioms.
The term abstrac algebra is used to distinguish this field fro elemental algebra of common school algebra where it shows the correct rules to manipulate the formulae and algebraic expressions that concern bith real and complex numbers.
Abstrac algebra includes:
· Quasigroups
· Semigroups
· Monoids
· Groups
· Integrity domains
· Rings and bodies
· Modules and vector spaces
· Associative algebra and Lie algebra
· Reticules and Boole algebras
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