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  2. Abstract algebra - Wikipedia

    en.wikipedia.org/wiki/Abstract_algebra

    Abstract algebra. The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra. 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 ...

  3. Abstract algebraic logic - Wikipedia

    en.wikipedia.org/wiki/Abstract_algebraic_logic

    Abstract algebraic logic is a modern subarea of algebraic logic that emerged in Poland during the 1950s and 60s with the work of Helena Rasiowa, Roman Sikorski, Jerzy Łoś, and Roman Suszko (to name but a few). It reached maturity in the 1980s with the seminal publications of the Polish logician Janusz Czelakowski, the Dutch logician Wim Blok ...

  4. Commutator subgroup - Wikipedia

    en.wikipedia.org/wiki/Commutator_subgroup

    Commutator subgroup. In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. [1][2] The commutator subgroup is important because it is the smallest normal subgroup such that the quotient group of the original group by this ...

  5. List of abstract algebra topics - Wikipedia

    en.wikipedia.org/wiki/List_of_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 ...

  6. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements 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.

  7. Representation theory - Wikipedia

    en.wikipedia.org/wiki/Representation_theory

    Representation theory studies how algebraic structures "act" on objects. A simple example is how the symmetries of regular polygons, consisting of reflections and rotations, transform the polygon. Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations ...

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