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In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [1] Algebraic structures include groups , rings , fields , modules , vector spaces , lattices , and algebras over a field .
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 ...
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Pages in category "Abstract algebra" The following 143 pages are in this category, out of 143 total. This list may not reflect recent changes. ...
The passage from classical algebraic logic to abstract algebraic logic may be compared to the passage from "modern" or abstract algebra (i.e., the study of groups, rings, modules, fields, etc.) to universal algebra (the study of classes of algebras of arbitrary similarity types (algebraic signatures) satisfying specific abstract properties).
Pages in category "Fields of abstract algebra" This category contains only the following page. This list may not reflect recent changes. W. Wheel theory
Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures has been formalized in universal algebra . Category theory is another formalization that includes also other mathematical structures and functions between structures of the same type ( homomorphisms ).
An algebra is called a simple algebra if it does not contain a nontrivial two sided ideal. The general pattern is that the structure admits no non-trivial congruence relations. The term is used differently in semigroup theory. A semigroup is said to be simple if it has no nontrivial ideals, or equivalently, if Green's relation J is the ...