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Instructions for Doctoral Dissertation Proposal Form

For applicants

  1. The proposal form must be filled by typing in the MS Word format using BOLD letters of Arial font with the font size of 12.
  2. Fill out the list of the dissertation committee on page (D 4).
  3. Attach an appendix to the proposal form (not exceeding 10 pages on A4 paper) with the following information:

3.1Name, ID number, department, program of study and number of dissertation credits (on the first page)

3.2Rationales, theories or assumptions (in detail)

3.3Research methodology

3.4Experimental procedures (in detail)

3.5References

4. Submit the completed proposal form to the dissertation advisor for approval before proceeding to Step 5.

5.Defend the proposal.

6.The approved proposal must be signed by the applicant, dissertation advisor, program chair and program secretary.

7.Fill out the proposal information at

8.Submit the signed proposal form to the Bureau of The Education Management Section, Faculty of Science, Room 103, Tab building.

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Note: The most updated proposal can bedownloaded from

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Doctoral Dissertation Proposal

Faculty of Science, ChulalongkornUniversity

First Name Apirat Last NameSiraworakun ID5173878223

Department Mathematics and Computer Science ProgramMathematicsDissertation Credits48

Academic Curriculum RegularPart-Time English Program International Program

Enrolled Since  First Second SemesterAcademic Year2008

Contact Address 827 Vilijit Road, Bangputha, Muang, Singburi 16000

Telephone Number 0891524834

Dissertation Title (Thai)

ไฮเพอร์มอดูลย่อยเฉพาะและเฉพาะอย่างอ่อนและไฮเพอร์มอดูลย่อยฟัสสิเฉพาะ

Dissertation Title (English --Capital letters)

PRIME AND WEAKLY PRIME SUBHYPERMODULES AND PRIME FUZZY SUBHYPERMODULES

Dissertation AdvisorAssistantProfessor Dr.Sajee PianskoolTel. 022185144

Co-advisor Professor Dr.Mark Edwin Hall

Signature………………………………….(Applicant)

Date……./……/……

Signature………….……………… Signature…………………………

Dissertation Advisor (...... )

Date……./……/…… Program Chair

Date……./….…/….…

Approval from the Program committee of……………….…...Meeting No…..../…….Date…..……
Signature……………………………………….
ProgramSecretary of the Ph.D Program in…………….……………..
Date……./……/……
Approval from the Faculty Administrative Committee meeting no……..…….Date………………..
Signature……………………….………………………….

Associate Dean, Faculty of Science

Date……./……/……

(D 2)

Doctoral Dissertation Proposal

Faculty of Science Administrative Committee

First Name Apirat Last NameSiraworakun ID5173878223

Department Mathematics and Computer Science ProgramMathematics Dissertation Credits48

Academic Curriculum RegularPart-Time English Program International Program

Enrolled Since  First Second SemesterAcademic Year2008

Contact Address 827 Vilijit Road, Bangputha, Muang, Singburi 16000

Telephone Number 0891524834

Dissertation Title (Thai)

ไฮเพอร์มอดูลย่อยเฉพาะและเฉพาะอย่างอ่อนและไฮเพอร์มอดูลย่อยฟัสสิเฉพาะ

Dissertation Title (English --Capital letters)

PRIME AND WEAKLY PRIME SUBHYPERMODULES AND PRIME FUZZY SUBHYPERMODULES

Dissertation AdvisorAssistant Professor Dr.Sajee Pianskool

Co-advisorProfessor Dr.Mark Edwin Hall

Objectives

  1. To give some properties of prime subhypermodules and weakly prime subhypermodules.
  2. To characterize prime subhypermodules and weakly prime subhypermodules.
  3. To study fuzzy subhypermodules and prime fuzzy subhypermodules.

Rationales, Theories, or Assumptions

It can be seen from many literatures that the idea for prime submodules of a module is derived from the concept of prime ideals of a ring. There are some relations between these, for example, a prime ideal of a ring R is a prime submodule of the R-module R. Prime submodules play an important role in several work related to submodules; in addition, prime submodules have been generalized in many ways, such as weakly prime submodules.

The theory of hyperstructures (also called multialgebras) started with the communication of F. Marty in 1934 at the 8th Congress of Scandinavian Mathematicians. P.Corsini gathered the fundamental concepts of those in his book “Prolegomena of hypergroup theory”.There have been many research papers on hyperstructures since then.

In this research, we study one type of hypermodules over a hyperring. We also give a definition of prime subhypermodule of a hypermodule and investigate some properties. Then we generalize this definition to a weakly prime subhypermodule and determine relations between these two. The main results are characterizations of prime and weakly prime subhypermodules in many contexts. Finally, we introduce fuzzy subhypermodules and prime fuzzy subhypermodules of a hypermodule. Many properties are investigated

Research Methodology

  1. Study research work on prime submodules and weakly prime submodules.
  2. Study research work on fuzzy submodules and fuzzy prime submodules.
  3. Investigate some properties of prime subhypermodules , weakly prime subhypermodules and some relations among them.
  4. Study fuzzy subhypermodules and fuzzy prime subhypermodules.
  5. Write research articles and a dissertation.

(D 3)

Research Plan

Use straight lines (no arrows)in numbered spacesto represent the period of time (in months) for each step to complete the dissertation)

Step / Description
(Dissertation started in November, 2010) / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20 / 21 / 22 / 23 / 24
1 / Study research workon prime submodules and weakly prime submodules. /
2 / Study research workon fuzzy submodules and fuzzy prime submodules. /
3 / Investigate some properties of prime subhypermodules, weakly prime subhypermodules and some relations among them. /
4 / Study fuzzy subhypermodules and fuzzy prime subhypermodules. /
5 / Write research articles and a dissertation. /

Expected beneficial outcome(s) from the dissertation

The following will be obtained :

  1. some properties of prime subhypermodules, weakly prime subhypermodules and some relations between them;
  2. characterization of prime subhypermodules, weakly prime subhypermodules;
  3. some properties of fuzzy subhypermodules and fuzzy prime subhypermodules.

Signature……………………………………(Applicant)

Date……../…...../……..

(D 4)

Appendix

Doctoral Dissertation Committee Nomination

First Name Apirat Last NameSiraworakun ID5173878223

Department Mathematics and Computer Science ProgramMathematics Dissertation Credits48

Academic Curriculum RegularPart-Time English Program International Program

Enrolled Since  First Second SemesterAcademic Year2008

Contact Address 827 Vilijit Road, Bangputha, Muang, Singburi 16000

Telephone Number 0891524834

Dissertation Title (Thai)

ไฮเพอร์มอดูลย่อยเฉพาะและเฉพาะอย่างอ่อนและไฮเพอร์มอดูลย่อยฟัสสิเฉพาะ

Dissertation Title (English --Capital letters)

PRIME AND WEAKLY PRIME SUBHYPERMODULES AND PRIME FUZZY SUBHYPERMODULES

List of Doctoral Dissertation Committee

Program Chair or Appointed Personnel by the ChairChair

Assistant Professor Dr.Sajee Pianskool Advisor

Professor Dr.Mark Edwin Hall(1) Co-advisor

Associate Professor Dr.AmornWasanawichit Committee

Assistant Professor Dr.Yotsanan MeemarkCommittee

Associate Professor Dr.Utsanee Leerawat(2)Committee(external)

………………………………(Program Chair)

Date……../…...../……..

(1)Department of Mathematics and Computer Science, Hasting College, USA

(2)Department of Mathematics, Faculty of Science, Kasetsart University

Note: The doctoral dissertation committee consists of 5-7 people. The committee must consist of the program chair or an appointed personnel by the chair, the advisor and co-advisor(s) (if any, counted altogether as one committee member), two academic staffs of ChulalongkornUniversity and at least one external committee from outside ChulalongkornUniversity. If the program chair is the advisor or a co-advisor, the chair must be assigned to the other.
Example (D 4)

Appendix

Doctoral Dissertation Committee Nomination

First Name Dutsadee Last Name PitiID 5075555523

Department-ProgramBiological Science Dissertation Credits 48

Academic Curriculum RegularPart-TimeEnglish Program International Program

Enrolled since First Second SemesterAcademic Year2552

Dissertation Title (Thai)

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Dissertation Title (English -- Capital letters)

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List of Doctoral Dissertation Committees

Program Chair or Appointed Personnel by the Chair Chair

Professor Dr. Somsak PunhaAdvisor

Professor Dr. Henrik Enghoff (1)Co-advisor

ProfessorDr. AnchaleeTassanakhachornCommittee

Assistant Professor Dr.TorsakSeelanantCommittee

Dr. Piyorot ThongkerdCommittee

ProfessorDr. Wisut Baimai(2)Committee(external)

………………………………(Program Chair)

Date……../…...../……..

(1)Natural History Museum of Denmark, University of Copenhagen

(2)Department of Biology, Faculty of Science, MahidolUniversity(Retired government employee)

Note: The doctoral dissertation committee consists of 5-7 people. The committee must consist of the program chair or an appointed personnel by the chair, the advisor and co-advisor(s) (if any, counted altogether as one committee member), two academic staffs of ChulalongkornUniversity and at least one external committee from outside ChulalongkornUniversity. If the program chair is the advisor or a co-advisor, the chair must be assigned to the other.