The question really is- how important is it to you to know exactly how this man died? If it's very important to you, then perhaps you should ask his widow directly, since she used to be your friend. If asking her would make you uncomfortable, then maybe you are not close enough to the family to actually need to know all the details.
Yes Alzeimer's can kill, as well as pneumonia. Depression and bi-polar disorder 'kill' too- if the sufferer decides to take their own life.
Expressing your condolences through a card or a phone call, without inquiring about the details of his death would be tactful.