Angular2 app module with root level imports

Shouldn't imports on the root level be available globally (With globally I mean to all sub-modules and components)?

I have the following root/app module :

import { BrowserModule } from '@angular/platform-browser';
import { NgModule, ApplicationRef } from '@angular/core';
import { CommonModule } from '@angular/common';
import { FormsModule } from '@angular/forms';
import { AppComponent } from './app.component';
import { HttpModule } from '@angular/http';
import { RouterModule } from '@angular/router';
import { appRouterProviders, routing } from './app.routes';
import { DashboardModule } from './dashboard/dashboard.module';
import { DecisionModule } from './decision/decision.module';
import { MdCoreModule }           from '@angular2-material/core';
import { MdButtonModule }         from '@angular2-material/button';
import { MdCardModule }           from '@angular2-material/card';
import { MdListModule }           from '@angular2-material/list';
import { MdSidenavModule }        from '@angular2-material/sidenav';
import { MdToolbarModule }        from '@angular2-material/toolbar';
import { MdIconModule }           from '@angular2-material/icon';

@NgModule({
  declarations: [
    AppComponent                    
  ],
  imports: [
    BrowserModule,
    CommonModule,
    FormsModule,
    HttpModule,
    RouterModule,    
    routing,
    DashboardModule,
    MdCoreModule,
    MdButtonModule,
    MdCardModule,
    MdListModule,
    MdSidenavModule,    
    MdToolbarModule,
    MdIconModule
  ],
  providers: [
    appRouterProviders
  ],
  entryComponents: [ AppComponent ],
  bootstrap: [ AppComponent ]
})
export class AppModule {

}

If I try to use the material elements in one of my sub modules they don't display, this is what the sub module looks like:

import { NgModule }               from '@angular/core';
import { CommonModule }           from '@angular/common';
import { FormsModule }            from '@angular/forms';
import { dashboardRouting }       from './dashboard.routes';
import { DashboardComponent }     from './dashboard.component';
import { ActionsDialogComponent } from './actions-dialog';

@NgModule({
  imports: [
    CommonModule,
    FormsModule,
    dashboardRouting,    
  ],
  declarations: [
    DashboardComponent,
    ActionsDialogComponent    
  ],
  providers: [    
  ]
})
export class DashboardModule {}

However if I import the material modules in the submodule they display. This is what the submodule looks like when the material design components work:

import { NgModule }               from '@angular/core';
import { CommonModule }           from '@angular/common';
import { FormsModule }            from '@angular/forms';
import { dashboardRouting }       from './dashboard.routes';
import { DashboardComponent }     from './dashboard.component';
import { ActionsDialogComponent } from './actions-dialog';
import { MdCoreModule }           from '@angular2-material/core';
import { MdButtonModule }         from '@angular2-material/button';
import { MdCardModule }           from '@angular2-material/card';
import { MdListModule }           from '@angular2-material/list';
import { MdSidenavModule }        from '@angular2-material/sidenav';
import { MdToolbarModule }        from '@angular2-material/toolbar';
import { MdIconModule }           from '@angular2-material/icon';

@NgModule({
  imports: [
    CommonModule,
    FormsModule,
    dashboardRouting,
    MdCoreModule,
    MdButtonModule,
    MdCardModule,
    MdListModule,
    MdSidenavModule,    
    MdToolbarModule,
    MdIconModule,
  ],
  declarations: [
    DashboardComponent,
    ActionsDialogComponent    
  ],
  providers: [    
  ]
})
export class DashboardModule {}

Why must the material modules be imported on the sublevel again if they are already imported at the root level?

In the concept of Components in Angular2 there is nothing like a "root level" to which you are referring.
Components are modular pieces very much like Classes in a Java (or whatever High level language) project - where you would also import every Class you use.
They can be nested or used inside each other, but still every components needs to import its own dependencies.
Please note that importing in Angular2 is a very different approach than including a external module/library was in Angular 1 (then essentially beeing a new reference in index.html for each dependency).
Those imports in Angular 2 are there first, because the Typescript-compiler needs to know what is used in your component (thus adding some more power to do error checking)
The compiled and packaged build should include every dependency just once (provided everything is configured correctly).