A generalization of Cohen's theorem

A GENERALIZATION OF COHEN’S THEOREM

NGUYEN TRONG BAC

A THESIS SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY (MATHEMATICS)

FACULTY OF GRADUATE STUDIES

MAHIDOL UNIVERSITY

2015

COPYRIGHT OF MAHIDOL UNIVERSITY

Thesis

entitled

A GENERALIZATION OF COHEN’S THEOREM

……………….………….…..………

Mr. Nguyen Trong Bac

Candidate

………………….…..………….……

Lect. Nguyen Van Sanh,

Ph.D. (Mathematics)

Major advisor

………………….…..………….……

Asst. Prof. Chaiwat Maneesawarng,

Ph.D. (Mathematics)

Co-advisor

………………….…..………………..

Lect. Somsak Orankitjaroen,

Ph.D. (Mathematics)

Co-advisor

………………….…..…………

Prof. Patcharee Lertrit,

M.D., Ph.D. (Biochemistry)

Dean

Faculty of Graduate Studies

Mahidol University

………………….…..……………..…

Asst. Prof. Duangkamon Baowan,

Ph.D. (Mathematics)

Program Director

Doctor of Philosophy Program in

Mathematics

Faculty of Science, Mahidol University

Thesis

entitled

A GENERALIZATION OF COHEN’S THEOREM

was submitted to the Faculty of Graduate Studies, Mahidol University

for the degree of Doctor of Philosophy (Mathematics)

on

October 02, 2015

……………….………….…..………

Mr. Nguyen Trong Bac

Candidate

………………….…..………………

Prof. Phan Dan,

Ph.D. (Mathematics)

Chair

………………….…..………….……

Lect. Nguyen Van Sanh,

Ph.D. (Mathematics)

Member

………………….…..……...

Lect. Somsak Orakitjaroen,

Ph.D. (Applied Mathematics)

Member

………………….…..………………..

Asst. Prof. Chaiwat Maneesawarng,

Ph.D. (Mathematics)

Member

………………….…..……...

Prof. Patcharee Lertrit,

M.D., Ph.D. (Biochemistry)

Dean

Faculty of Graduate Studies

Mahidol University

………………….…..……………..…

Prof. Skorn Mongkolsuk,

Ph.D. (Biological Science)

Dean

Faculty of Science

Mahidol University

iii

ACKNOWLEDGEMENTS

Firstly, I express my sincere gratitude and appreciation to my major

advisor, Dr. Nguyen Van Sanh for his guidance and advice.

I am also grateful to my co-advisors, Asst. Prof. Dr. Chaiwat Manee￾sawarng and Dr. Somsak Orankitjaroen, for their helpful guidance and encourage￾ment. I would like to thank Prof. Dinh Van Huynh from Ohio State University,

Prof. Dr. Hai. Q. Dinh and Prof. Dr. Artem Zvavitch from Department of Math￾ematical Sciences-Kent State University, Ohio, USA for their recommendation and

encouragement.

I would like to express my deep to the Department of Mathematics,

Mahidol University, for providing me necessary facilities and financial support. I

am very grateful to Thai Nguyen University of Economics and Business Admin￾istration and Thai Nguyen University of Sciences for the recommendation and

encouragement. Special thanks to Assoc. Prof. Dr. Tran Chi Thien, Assoc. Prof.

Nong Quoc Chinh, Assoc. Prof. Le Thi Thanh Nhan, Dr. N. T. Thu Thuy from

Thai Nguyen University and Assoc. Prof. T. X. Duc Ha from Institute of Mathe￾matics for their help and encouragement.

I greatly appreciate all my friends for their kind help throughout my

study at Mahidol University. Special thanks go to Mr. Isaac Defrain, Ms. Laura

Brewer, Ms. Virginia, Mr. Ping Song for warm hospitality and kind friendship

during my visit in the USA and Europe. I would like to thank every one in our

research group at Mahidol University under leading of Dr. N. V. Sanh and algebra

seminar group at Kent-State University. I will never forget our interesting semi￾nars.

Finally, I would like to use this thesis as a gift to my father, my mother

and my small family.

Nguyen Trong Bac