In C#, a Singleton is typically implemented by making the class constructor private and exposing a public static method to retrieve the single instance. Here's a simple example:

public class Singleton
{
    private static Singleton instance;   

       private Singleton() { }   

       public static Singleton Instance
    {
        get
        {
            if (instance == null)
            {
                instance = new Singleton();
            }
            return instance;
        }
    }
}

Pros:

1. Global Access: Singletons provide a single point of access to an instance, ensuring consistent behavior across the application.

2. Lazy Initialization: The instance is created only when needed, optimizing resource usage.

3. Prevents Multiple Instances: Guarantees that there's only one instance of the class, avoiding unintended consequences of multiple copies.

Cons:

1. Global State: Singleton introduces a global state, which can lead to tight coupling and reduced testability.

2. Harder to Test: Dependencies on a Singleton can make unit testing more challenging due to the global state.
   
   

When to Use and When Not:

• Use: When exactly one instance is required, and providing a global point of access is beneficial.

• Avoid: In scenarios where a global state can lead to unforeseen issues or when testing and maintainability are top priorities.
  
  

Usage in .NET Core Framework:

The Singleton Pattern is prevalent in the .NET Core framework, notably in services registered as singletons within the Dependency Injection (DI) container. For instance, in ASP.NET Core, services like database contexts or configuration settings are often registered as singletons to ensure a single instance shared across the application.

Real-Life Example:

Consider a logging service in a gaming application. The Singleton pattern ensures there's a single logger instance to handle logs throughout the game. This not only centralizes logging logic but also prevents the creation of multiple loggers, optimizing resource usage.

In conclusion, the Singleton Pattern in C# is a powerful tool for managing instances in a controlled manner. While it offers global access and lazy initialization, developers should be mindful of potential downsides like global state and reduced testability. Understanding when to use it and where it's employed in the .NET Core framework can help harness its benefits effectively in real-world scenarios.

In the .NET Core framework, you can register a singleton in the Dependency Injection (DI) container during application startup. Here's an example of how to register a singleton:

Assuming you have a class MySingletonService that you want to register as a singleton, follow these steps:

1. Create the Singleton interface and the implementation:
   public class MySingletonService{// Your singleton implementation goes here}
   
   
2. Register the Singleton Service with the Framework:
   services.AddSingleton<MySingletonService>();