Publish a significant but brief improvement of a Mathematics paper I am a PhD student and I started studying a recent article of my advisor. During the study, I realized that some of the reasonings and results used in the article could be considerably improved. Moreover, the result of the main theorem of the paper could have been much more general. My advisor agrees on this.

Thus, the changes are significant. The problem is that the novelty of the idea belongs to the previous paper and that my changes, although significant, would be 4 or 5 pages of length (the original article is 10 pages length).

My question is whether significant but brief improvements of papers in the field of Mathematics can be published in some journals. Should I forget about this idea? Should I send the improved version to the same journal than the previous paper? Are there special journals for papers dealing with significant but brief improvements of extant articles?
Mathematics is about solving problems, not extensive writing!

The briefer the better, the significance is even better.

There are lots of publications of novel proofs of the same theorem, just of the sake of development!