Can a Singleton Class inside a DLL be shared across processes?

I am creating a custom .net hardware framework that will be used by other programmers to control some hardware. They will add a reference to our DLL to get to our hardware framework. I am in need of a shared class that will be accessed from multiple applications (processes).

The singleton pattern seems to be what I need but it only works for multiple threads inside your process. I could be completely wrong but here is an example of the C# code I currently have. I can't help to feel that the design is incorrect. I wish I could share more specific information but I can't.

• I must stress that I will have no control over the customer application. The solution must be contained inside the framework (DLL) itself.

The Framework: (Shared DLL)

public class Resources
{
    static readonly Resources m_instance = new Resources();

    public string Data;

    private Resources()
    {
        Data = DateTime.Now.ToString();
    }

    public static Resources Instance
    {
        get
        {
            return m_instance;
        }
    }
} 

The Test Application: (eventually customer app)

class Program
{
    static void Main(string[] args)
    {
        Console.WriteLine("Press enter to capture the resource!");
        Console.ReadLine();

        var resources = Resources.Instance;
        Console.WriteLine("\r\n{0}: {1}\r\n", Thread.CurrentThread.ManagedThreadId, resources.Data);

        BackgroundWorker worker = new BackgroundWorker();
        worker.DoWork += WorkerDoWork;
        worker.RunWorkerAsync();

        while (worker.IsBusy)
        {
            Thread.Sleep(100);
        }

        Console.WriteLine("Press enter to close the process!");
        Console.ReadLine();
    }

    static void WorkerDoWork(object sender, DoWorkEventArgs e)
    {
        var resources = Resources.Instance;
        Console.WriteLine("\r\n{0}: {1}\r\n", Thread.CurrentThread.ManagedThreadId, reso