Trust management and trustworthy computing are becoming increasingly significant at present. Over the recent years there have been several research works that have addressed the issue of trust management in distributed systems. However a clear and comprehensive definition that can be used to capture a range of commonly understood notions of trust is still lacking. In this paper, we give a formal definition of trust relationship with a strict mathematical structure that can not only reflect many of the commonly used extreme notions of trust but also provides a taxonomy framework where a range of useful trust relationships can be expressed and compared. Then we show how the proposed structure can be used to analyze both commonly used and some unique trust notions that arise in distributed environments. This proposed trust structure is currently being used in the development of the overall methodology of life cycle of trust relationships in distributed information systems.