Can a patent exclude others from patenting an improvement?

Most patents are effectively improvement patents - technology usually builds or improves upon previous technology, so the short answer is yes, a patent could be obtained for an improvement. Let's explore a simple scenario and you will better appreciate patents and their commercialization. Let's say Mr. A develops the first chair ever - he claims his chair broadly as comprising a seat, a back, and at least one leg - it could be a pedestal type leg.
Mr. B comes along and decides to place a cushion upon the seat so as to render the chair more comfortable. He obtains a patent for this improvement - a seat, a back, at least one leg, and a seat cushion. Now, the problem is that Mr. B can't market his own improved chair without infringing Mr. A's patent because even if Mr. B's chair contains his seat cushion, it also contains a seat, a back, and at least one leg - therefore his chair, even with the seat cushion, contains all of the elements of Mr. A's broadest claim which comprises a seat, a back, and at least one leg. However, on the other hand, Mr. A appreciates the fact that Mr. B's chair is an improvement and would probably sell better than his chair because it's more comfortable, but Mr. A can't manufacture Mr. B's chair without infringing Mr. B's patent - so what to do? They cross-license each other permitting each one to manufacture either or both chairs without either one of them infringing the other's patent. Therefore, if you have a patent on the basic technology, someone with an improved product and patent cannot manufacture it without some agreement - license or whatever - with you so as not to infringe your patent.