ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR QUARTERLY REPORT NO. 2 (Covering Period February 1, 1954 - April 30,.1954) By ROBERT Project M. THRALL Supervisor JAMES P. JANS: JOHN WALTER Project 2200 DETROIT ORDNANCE DISTRICT, ORDNANCE CORPS, U. S. ARMY CONTRACT DA-20-018-ORD-13281, DA PROJECT NO. 599-01-004 ORD PROJECT NO. TB2-001-(1040), OOR PROJECT NO. 31-124 May, 1954

- ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN QUARTERLY REPORT NO, 2 INTRODUCTION Work on this project has continued along the lines indicated in Quarterly Report No. 1. As indicated below, the dissertations of Jans and Walter have been essentially completed and are being submitted as technical reports. They will continue with their respective programs of research. In addition, other workers will be added to the project's staff during the summer and the research activities will be considerably expanded during this period. PROGRESS REPORT OF JAMES P. JANS The summary of the past three months' activities is as follows. The research for the dissertation previously mentioned has been completed. Three new conditions on the- structure of an algebra have been discovered which determine that it has an infinite number of inequivalent, indecomposable representations of a certain degree for each of an infinite number of degrees. The work on the final draft is now in progress and should be completed within a month, PROGRESS REPCRT OF JOHN WALTER During the last three months the following activities have been pursued. First, the dissertation on the automorphism of the projective unitary groups has been completed and has been submitted as a technical report, "Automorphisms of the Projective Unitary Groups", Engineering Research Institute, Report Namber 2200-2-T- University of Michigan, Ann Arbor. Second, progress has been made in the study of nonsemisimple commutative algebras. The 1

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN work of Taketa, which was mentioned in the last report, has been investigated further. It appears that Taketa's analysis is incomplete. Instead of continuing with Taketa's approach, greater emphasis is being placed on finding relations between the intrinsic structure of the algebras and their representations. In particular, closer attention is being paid to ideal theory. The remaining time spent on the project will be devoted to the study of these algebras. i 2

DISTRIBUTION LIST 3 Office of Ordnance Research Box CM, Duke Station Durham, North Carolina 2 Office, Chief of Ordnance Washington 25, D, C, Attention: ORDTB-PS 2 Chief, Detroit,. Ordnance District 574 East Woodbridge Detroit 31, Michigan Attention: ORDEF-IM 5