Master's level computer science programs have experienced significant and sustained growth during the past two decades. According to the U.S. Department of Education's National Center for Education Statistics [4], a total of 1,588 master's degrees were conferred in computer and information sciences in 1971. This figure increased 508% to 8,070 in 1986—a larger percentage increase than any other major discipline. The 1970s and 1980s have also been an era in which computer science has experienced major theoretical and technological advances. The period has been marked by severe faculty shortages which are only now beginning to ease. Complicating matters further, the discipline is so young that it is still in the process of defining its intellectual framework [3]. Considering all of these factors, it is not surprising that there is a considerable amount of diversity and flux among computer science master's programs. What is surprising, however, is that little data is available pertaining to this degree.
Perfect rings, minimal injective cogenerator, minimal projective resolutions, injective projective modules, codominant and dominant dimensions, generalized uniserial rings, Kupisch sequences. (1) This paper is taken from the author's doctoral dissertation written under the direction of Professor F. W. Anderson at the University of Oregon while the author was a National Science Foundation Graduate Fellow. The author wishes to express his appreciation to Professor Anderson for his guidance and encouragement.
Continuing an earlier examination of the codominant dimension of rings and modules, a categorical characterization is given for rings of equivalent dominant and codominant dimensions. Specifically, the question is teduced to when RR and the left minimal injective cogenerator 11 can be used as test modules respectively for the dominant dimension of the projective modules and the codominant dimension of the injective modules. These conditions are in turn characterized by when the injective projective modules are 2-injective. Also, a new and shortened version is given for the proof that the codominant dimension of the injective modules is equal to the dominant dimension of the projective modules.
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