Unit testing abstract generic classes

I have a generic abstract class with some methods like:

public abstract class MasterDataViewModel<TPrimaryModel> : ViewModel
    where TPrimaryModel : TwoNames, new()
{
    public void New()
    {
        PrimaryModel = new TPrimaryModel();
        Address = new Address();
        RaisePropertyChanged(String.Empty, validatePropertyName: false);
        ViewMode = ViewMode.New;
    }

    public void Save()
    {
        ...
    }
}

This base abstract class is derived a couple of times. I think it's not possible/good to unit test the abstract class directly. My idea was to write an abstract generic unit test class for the class like:

[TestClass]
public abstract class MasterDataViewModelTest<TPrimaryModel>
    where TPrimaryModel : TwoNames, new()
{
    #region Properties
    protected MasterDataViewModel<TPrimaryModel> ViewModel; 
    #endregion

    [TestClass]
    public class NewCommand : MasterDataViewModelTest<TPrimaryModel>
    {
        /// <summary>
        /// New command "clears" all content of the viewmodel
        /// </summary>
        [TestMethod]
        public void Execute()
        {
            //Arrange
            TPrimaryModel primaryModel = new TPrimaryModel();

            ////Fill view model with "random" values
            const string name = "Just a string";
            ViewModel.SearchTerm = name;
            ViewModel.Name1 = name;
            ViewModel.Name2 = name;
            ...

            ////Set view mode to "random" value
            ViewModel.ViewMode = ViewMode.Edit;

            //Act
            ViewModel.NewCommand.Execute(null);

            //Assert
            Assert.AreEqual(ViewMode.New, ViewModel.ViewMode);

            Assert.IsTrue(String.IsNullOrEmpty(ViewModel.SearchTerm));
            Assert.IsTrue(String.IsNullOrEmpty(ViewModel.Name1));
            Assert.IsTrue(String.IsNullOrEmpty(ViewModel.Name2));
            ...
        }
    }
}

For every derived class of my MasterDataViewModel I could write a unit test class which derives from my abstract unit test class:

[TestClass]
public class RecipientViewModelTest : MasterDataViewModelTest<Recipient>
{

}

By doing so I hoped that this class would "get" all tests from the base unit test class automatically and I could execute those tests.

Is this technically possible? And is this an approach you can recommend? Or are there better approaches?