“…և S be surjective homomorphisms of rings. Recently, the study of the fiber product rings R × T S has been an effective topic of investigation by several authors in different subjects, for instance, structural results [1,11,8,24,26], homological problems [13,16,23,17,21,24,25], and their geometric aspects [14,15]. Actually, most of these works consider the case T = k, and this provides a good understanding of the structure of R × k S. When T = k, few results are known and this motivate us the investigation showed here.…”