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Generalized regular rings and semiprimary group rings

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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.

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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.

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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

References

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