I got an email supposedly from Amazon saying that someone in China tried to access my account [View all]

Just to clarify, I ordinarily don't do Amazon but I did have a couple of gift cards a dear friend had given me and once I did buy an Amazon gift card for another dear friend who loves it. Anyway, the email looked very convincing, it even had amazon.com as its address but I never click on links I'm not sure about. Besides it began the email with "Dear Customer" and not with my name, so that immediately made me think it wasn't legit. About a week later, I got another email saying that my account has been locked and to follow the link to unlock it or else go to my account and follow the instructions. Again, I didn't click on the link; instead I went to Amazon's website and got on my account with no problem. It didn't look locked to me so I think I did the right thing by ignoring those emails. But I have to say, they sure made them look like they were legitimately from Amazon.