Quotient Modules

Construction of Quotient Modules

quo<M | L>: ModTupRng, List -> ModTupRng

quo<M | L>: ModMatRng, List -> ModMatRng

Given an \(R\)-module \(M\), construct the quotient module \(P = M/N\), where \(N\) is the submodule generated by the elements of \(M\) specified by the list \(L\). Each term \(L_i\) of the list \(L\) must be an expression defining an object of one of the following types:

(a)

A sequence of \(n\) elements of \(R\) defining an element of \(M\);

(b)

A set or sequence whose terms are elements of \(M\);

(c)

A submodule of \(M\);

(d)

A set or sequence whose terms are submodules of \(M\).

The generators constructed for \(N\) consist of the elements specified by terms \(L_i\) together with the stored generators for submodules specified by terms of \(L_i\).

The constructor returns the quotient module \(P\) and the natural homomorphism \(f : M \rightarrow P\).