Unital left and right modules over a ring; unqualified module means left module

Depends on

• Ring: an abelian group under addition and a monoid under multiplication, with multiplication distributing over addition on both sides
• Group and abelian group

Used by

• Exact finite tensor functors have projective right-module kernels Corollary
• Graded bimodule maps classify shift-compatible transformations Corollary
• A Deligne kernel need not be one external tensor factor Counterexample
• A right exact module functor without coproduct preservation is not tensor Counterexample
• An infinite-dimensional dual algebra with a nonrational module Counterexample
• The left-to-right exact equivalence need not preserve the identity Counterexample
• Weak actions do not supply pentagon coherence data Counterexample
• (S,R)-bimodules and commuting left and right scalar actions Definition
• A semisimple ring as a ring whose left regular module is semisimple Definition
• Additive cocontinuous module functors and their schematic category Definition
• An R-linear action of G on a left R-module, and a G-module over R Definition
• Annihilators, torsion elements and the torsion subset of a module Definition
• Arbitrary-level cyclotomic Hecke, Murphy cell and multipartition Schur modules Definition
• Balanced maps from a right module and a left module, and bilinear maps over a commutative ring Definition
• Cellular bases and cell modules Definition
• Cohomological left and right differential graded modules Definition
• Derivation of an algebra Definition
• Divisible modules over an integral domain Definition
• Finite based free complexes and contraction torsion Definition
• Koszul sign rule for graded tensor products and permutations Definition
• Left and right Artinian rings Definition
• Left and right Noetherian rings Definition
• Localisation of a module at a multiplicative subset Definition
• Module homomorphism and isomorphism, kernel, image and cokernel Definition
• Modules over a Hall algebra are unital algebra representations Definition
• Morse homology of a Morse--Smale pair Definition
• Noetherian commutative rings and modules Definition
• Quotient module M/N with scalar multiplication on additive cosets Definition
• Representations of unital associative algebras Definition
• Right-right Hopf modules and coinvariants Definition
• Simple module: a nonzero module with no proper nonzero submodule Definition
• Stable general linear and elementary groups for right modules Definition
• Submodule of a module Definition
• Support of a module Definition
• The annihilator of a module over an enveloping algebra Definition
• The category FI and FI-modules over a commutative ring Definition
• The continuation chain map Definition
• The direct sum of an indexed family of modules Definition
• The dual convolution algebra and rational modules Definition
• The F[x]-module V_T of an endomorphism Definition

…and 69 more results.

Dependency tree · two levels

8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• McGerty, Algebra II: Rings and Modules, Section 3 (standard reference, not scraped)