Branches centred on the three classical families of algebraic structure and on the methods that connect them. An entry belongs here when its cited source describes the study of groups and symmetry, of rings and their ideals, of fields and their extensions, or of the polynomial equations whose solutions these structures organise. It does not belong here when the branch is mainly about vector spaces and linear maps, about Lie theory and representations, or about categorical and homological machinery, which are grouped separately. The group follows the usual textbook sequence of abstract algebra, which moves from groups to rings to fields and then to Galois theory.
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Groups, Rings and Fields
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Group Theory (Wikipedia)
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In abstract algebra, group theory studies the algebraic structures known as groups.
Ring Theory (Wikipedia)
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In algebra, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers.
Field (mathematics) (Wikipedia)
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In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational numbers do.
Galois Theory (Wikipedia)
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In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory.
Commutative Algebra (Wikipedia)
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Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
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