module
generalization of vector space, with scalars in a ring instead of a field
algebra over a ring
module over a ring whose multiplication is bilinear
Hilbert C*-module
complex module E over a C*-algebra A equipped with an A-sesquilinear and complex-sesquilinear map ⟨–,–⟩: E×E→A that is nonnegative nondegenerate and satisfies the Cauchy–Schwartz inequality
abelian group
group whose group operation is commutative
completion
in algebra, any of several related functors on rings and modules that result in complete topological rings and modules
radical of a module
intersection of all maximal submodules; sum of all superfluous submodules
right module
module in which scalars are multiplied from the right
finitely generated module
In algebra, a module that has a finite generating set
bimodule
abelian group equipped with compatible ring action on both sides
tensor product of modules
operation that pairs a left and a right 𝑅‐module into an abelian group
localization of a module
construction to introduce denominators in a module for a ring
G-module
an abelian group
torsion-free module
module over a ring such that zero is the only element annihilated by a regular element of the ring
graded module
module decomposed into a direct sum of numbered submodules
quotient module
algebraic construction
cyclic module
module generated by one element
Clifford module
module over a Clifford algebra
Leibniz algebra
module over a commutative ring with a bilinear product [–, –] such that for any element x, [–, x] is a derivation
submodule
additive subgroup of a module closed under scalar multiplication
injective module
module that makes certain exact sequences split
almost ring
objects interpolating between rings and their fields of fractions
zero module
module that only contains 0
left module
module in which scalars are multiplied from the left