fractions_regular

I would like if sombody can tell me what it is known (or what he/she knows) about categories of fractions of regular categories. I imagine that if you have a calculus of right AND left fractions, then the category of fractions is regular, but what about if the calculus is only of right fractions ?. Any comments will be welcome. Greetings e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]