algebras.java

interface Semigroup<T> {
    T apply(T a, T b);
}

interface Monoid<T> extends Semigroup<T> {
    T identity();
}

interface Group<T> extends Monoid<T> {
    T inverse(T a);
}

class Ring<T> {
    public final Monoid<T> m;
    public final Group<T> a;

    public Ring(Monoid<T> m, Group<T> a) {
        this.m = m;
        this.a = a;
    }
}

class Field<T> {
    public final Group<T> m, a;

    public Field(Group<T> m, Group<T> a) {
        this.m = m;
        this.a = a;
    }
}