I made a summary book of a larger book and I provided it to my students six years ago. This derivative book has my name on it and was made without authorization of the editorial of the original book. It was not my intention to sell or profit from this, I wanted to provide my students with a summary of the important topics. I recently realized they published the document in websites like slideshare. I do not want the editorial to realize there is a derivative work online made without they authorization. Can I file a DMCA notice on my name, even if the document is not even registered legally on my name?
The answer is implicit in this, but the situation you described presents a complication. 17 USC 512(c)(3)(A) says what you must do to give an effective takedown notice:
To be effective under this subsection, a notification of claimed infringement must be a written communication provided to the designated agent of a service provider that includes substantially the following:
(i) A physical or electronic signature of a person authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.
(ii) Identification of the copyrighted work claimed to have been infringed, or, if multiple copyrighted works at a single online site are covered by a single notification, a representative list of such works at that site.
(iii) Identification of the material that is claimed to be infringing or to be the subject of infringing activity and that is to be removed or access to which is to be disabled, and information reasonably sufficient to permit the service provider to locate the material.
(iv) Information reasonably sufficient to permit the service provider to contact the complaining party, such as an address, telephone number, and, if available, an electronic mail address at which the complaining party may be contacted.
(v) A statement that the complaining party has a good faith belief that use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.
(vi) A statement that the information in the notification is accurate, and under penalty of perjury, that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.
When a person infringes copyright in the course of creating a derivative work, they still hold copyright in that derivative work (but they are liable for their illegal copying). On the other hand, if you just upload someone else's PDF, that is just bare infringement, and you are not the owner of an exclusive right.
There are statements that you could make about this which would be perjurous, and ones that you could make that would be truthful. If Smith originally wrote chapter 1 (Jones originally wrote chapter 2 etc.) and you massively rewrote all of these chapters, that could (should) provide the modicum of creativity required for there to be an exclusive right – the right in the present work (the one you are saying "take down!"). The things you have to swear to are the good faith belief that use of the material is unauthorized, and that you are authorized to act on behalf of the owner of an exclusive right. You should consult with your attorney to verify whether these statements (as you write them) are true.