Modules over Dedekind Domains
- Introduction
- Creation of Modules
Module(O, n): RngOrd, RngIntElt → ModDedModule(O, n): RngFunOrd, RngIntElt → ModDedModule(O): RngOrd → ModDed, MapModule(O): RngFunOrd → ModDed, MapModule(I): RngOrdFracIdl → ModDed, MapModule(I): RngFunOrdIdl → ModDed, MapModule(S): SeqEnum[Tup] → ModDed, MapModule(S): SeqEnum[RngOrdFracIdl] → ModDedModule(S): SeqEnum[RngFunOrdIdl] → ModDedModule(S): SeqEnum[ModElt] → ModDed, Map- Example: Creating Modules over Dedekind Domains
sub<M | m>: ModDed, SeqEnum[ModDedElt] → ModDed, Mapsub<M | m1, .., mn>: ModDed, ModDedElt, ..., ModDedElt → ModDed, Mapquo<M | S>: ModDed, ModDed → ModDed, Mapquo<M | m>: ModDed, SeqEnum[ModDedElt] → ModDed, Mapquo<M | m1, .., mn>: ModDed, ModDedElt, ..., ModDedElt → ModDed, Map- Example: Submodules and Quotient Modules
- Elementary Functions
- Predicates on Modules
- Arithmetic with Modules
I * M: RngOrdIdl, ModDed → ModDedI * M: RngFunOrdIdl, ModDed → ModDedM * I: ModDed, RngOrdIdl → ModDedM * I: ModDed, RngFunOrdIdl → ModDedM1 + M2: ModDed, ModDed → ModDedDirectSum(M1, M2): ModDed, ModDed → ModDed, Map, Map, Map, MapDirectSum(S): [ModDed] → ModDed, [Map], [Map]u * I: ModDedElt, RngOrdIdl → ModDedu * I: ModDedElt, RngFunOrdIdl → ModDedI * u: RngOrdIdl, ModDedElt → ModDedI * u: RngFunOrdIdl, ModDedElt → ModDed- Example: Module Arithmetic and Predicates
- Basis of a Module
- Other Functions on Modules
- Homomorphisms between Modules
hom<M -> N | T>: ModDed, ModDed, Map → Maphom<M -> N | T>: ModDed, ModDed, SeqEnum[ModTupRngElt] → Maphom<M -> N | T>: ModDed, ModDed, MtrxSpcElt → MapHom(M, N): ModDed, ModDed → ModDed, MapIsSubmodule(M, N): ModDed, ModDed → BoolElt, MapMorphism(M, N): ModDed, ModDed → Map- Example: Homomorphisms Between Modules over Dedekind Domains
- Elements of Modules
- Pseudo Matrices