Abstract
It will be the practice in this paper to use Barnes as the basis of terminology. Definitions not normally found in elementary algebra will be given. | As the title implies, the central theme of this paper is the study of coefficient fields in tensor products. In order to present a meaningful definition of a coefficient field, certain preliminary definitions are needed. It will be convenient to stipulate at the outset that certain "nice" conditions exist in the rings and fields with which we are working. Usually, this will mean that rings which we are considering contain a field K as a subring and that each has characteristic p /= o. We will further assume that the rings are communative with identity and that the identity of each of the rings and the field K coincide. Wherever applicable and unless otherwise specified, these conditions will prevail.