GENERALIZED REGULAR RINGS AND SEMIPRIMARY GROUP RINGS
VIM= Gupta
Thesis submitted to the Indian Institute of Technology,Delhi for the award of the Degree of
Doctor of Philosophy
Department of Mathematics
Indian Institute of Technology, Delhi
February 1975
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CERTIFICAM
This is to certify that the thesis entitled
"Generalized Regular Rings and Semiprimary Group Rings"
which is being submitted by Shri Vishnu Gupta for the award of Degree of Doctor of Philosophy (Mathematics)
to the Indian Institute of Technology, Delhi, is a record of bonafide research work. He has worked for the last three years under my guidance and supervision.
The thesis has reached the standard fulfilling the requirements of the regulations relating to the degree. The results in this thesis have not been submitted to any other University or Institute for the award of any degree or diploma.
SiOAX-Lokxsc,
( J.B. Srivastava ) Department of Mathematics
Indian Institute of Technology Hauz Maas, New Delhi-110029.
ACKNOWLEDGEMENTS
Firstly and most especially, I would like to
express my gratitude to Dr. J.B. Srivastava, Department of Mathematics, Indian Institute of Technology, Delhi, for encouragement, direction and stimulating discussions from which this work grew out.
I also owe thanks to Professors M.K. Jain,
K.R. Parthasarathy and M.P.'Singh, all of the Department of Mathematics,- Indian Institute of Technology, Delhi, for the interest they showed in my progress.
I thank all my colleagues and friends who have helped me during the preparation of this thesis.
Special thanks are also to Miss Neelam who did the typing.
1/431t
( Vishnu Gupta )
Department of Mathematics I.I.T., Delhi.
CONTENTS
CERTIFICATE ACKNOWLEDGEMENTS
INTRODUCTION
CHAPTER-I SEMI PR DIARY AND RESTRICTED SEMI- 1-19 PRIMARY GROUP RINGS
CHAPTER-II GENERALIZED REGULAR RINGS 20-46
CHAPTER-III THE MAXIMAL WEAKLY REGULAR 47-64 IDEAL OF A RING
CHAPTER-IV GROU P RINGS OF GENERALIZED 65-87 REGULAR RINGS