Can I apply for a patent for the improved product?

Whether you can apply for a patent depends on whether the content you want to apply for a patent has been published by other published products/documents. This requires case search (prior art search). If not, you can apply for a patent. If so, you need to make improvements to make the improved ones different from the public ones. The improved one can apply for a patent. No one on both sides prevents you from applying for a patent, that is to say, even if you know that the content you want to apply for a patent is public (already exists), you can apply for a patent, which is your right, but whether you can be granted a patent or claim a patent after being granted depends on whether it is public technology. On the issue of infringement, if you have a patent, then you have the right to prevent others from using your patented content without permission. That's all, there is no guarantee that you can make a patented product. For example, your patent is A+B+C three parts of anti-theft lock, in which c is your improvement. I have a patent for the A+B part of the anti-theft lock, and I applied for it first. At this time, if you make an anti-theft lock A+B+C according to your own patent, it is infringement and infringes on my patent, because my patent covers a wide range, as long as there are A and B, it is my patent.