I'd start with the correct spelling of architecture, especially if you want to teach. After that, try Google.

arthur, your question is so incredibly vague, the countdown's response seems almost warranted.

The second part of your question (online courses) is a bit more focused. There are plenty of schools that offer online courses for undergrad studies. Offering such courses for grad level education seems counter intuitive.

The NAAB (National Architectural Accrediting Board) lists 95 schools that offer MARCH degrees in the US.

I'm having a hard time figuring out why you are having such a hard time finding a program....

if you have a BArch - a professional degree - you'd be looking at MArch II programs - and most importantly, specific people with whom you'd like to study. If you haven't at least started developing research topics and a prelim thesis proposal(s) (which you can use to help narrow down individuals and programs), then I doubt you're even remotely prepared for a career in academia, let alone a post-professional masters degree.

If you are having trouble figuring out who is doing the kinds of research you are interested in, there are quite a few knowledgeable people on these forums - but you'll have to ask more targeted questions.

Lawrence Tech offers a online m. arch degree
Don't know if they offer an m. arch II

University of Michigan
post professional in research M.S. in Architecture
the description sounds like what you are looking for

also..

Columbia
M.S. in Critical, Curatorial and Conceptual Practices

both are research focused