Visualizing Finite Field of Order p2 through Matrices

 S. K. PANDEY Abstract- In order to introduce some new examples (other than those usually found in textbooks) on groups, rings and...

Global Journals Blog 2016

 S. K. PANDEY

Abstract- In order to introduce some new examples (other than those usually found in textbooks) on groups, rings and fields we usually make an attempt to create some examples. This helps to the students to learn the subject. If we just pose a question that write distinct examples of a finite field of order three. This creates curiosity and gives further insights into the subject. In the mathematical literature, the very common example of a finite field is Zp.

GJSFR: Global Journals Blog

One does not find any other example in the textbooks. This leads us to write two simple articles entitled ‘A Note on Matrix Representations of Finite Cyclic Groups’ [1] and ‘Matrix Field of Finite and Infinite Order’ [2].
In the mean time an idea evolved that we can easily yield a finite field of order p2 for every prime p≠2. This leads to write an article entitled ‘Visualizing Finite Field of Order p2 through Matrices’ [3] which has been recently published in the Global Journals. This article deals with a technique to produce a finite field p2 order without using the usual method of construction of finite fields.

The ideas to write above three articles evolved almost in a short period of time however it took years to realize the need to write and publish these works. 

This article ([3]) may be found useful for those working on Cryptography. There are always computational problems associated with the finite fields of higher orders. However in the case of a matrix field of finite order the addition and multiplication in the field reduce to the usual addition and multiplication of matrices. Since [3] can be used to create a finite matrix field of order p2 for each p>2 and therefore one can easily construct a finite field of as larger order as one needs to work.

In addition [3] is also useful to construct finite cyclic groups. Using the technique given in [3] one can yield a multiplicative cyclic group of order p2-1 for each p>2 .

Author’s Home Page Link: https://sites.google.com/site/skpandeysriram/home
 

REFERENCES RÈFÈRENCES REFERENCIAS

[1] S. K. Pandey, A Note on Matrix Representations of Finite Cyclic Groups, International Journal of Mathematics and Its Applications, 4(1-B), 2016, 27-28.
[2] S. K. Pandey, Matrix Field of Finite and Infinite Order, International Research Journal of Pure Algebra, 5(12), 2015, 214-216.
[3] S. K. Pandey, Visualizing Finite Field of Order p2 through Matrices, Global Journal of Science Frontier Research (F), Volume XVI, Issue 1, Version1, 2016, 27-30.

Research article:
https://globaljournals.org/GJSFR_Volume16/3-Visualizing-Finite-Field.pdf

Published by Global Journals
                                                © Global Journals Official Blog

COMMENTS

Name

Agriculture and Veterinary Biotech and Genetics Chemistry Environment and Earth Science Global Journal of Science Frontier Research Global Journals Global Journals Inc. Global Journals Inc. USA Global Journals Incorporated Interdisciplinary Marine Science Mathematics and Decision Science Physics and Space Science
false
ltr
item
Global Journals | Science Innovations & Stories Blog: Visualizing Finite Field of Order p2 through Matrices
Visualizing Finite Field of Order p2 through Matrices
https://1.bp.blogspot.com/-3a-iQdsif1U/Vyri41mn8rI/AAAAAAAAAn8/e3WzBNgxLUE7VBbzP8nmE-_9X48cm8-8QCLcB/s640/fractal-346127.jpg
https://1.bp.blogspot.com/-3a-iQdsif1U/Vyri41mn8rI/AAAAAAAAAn8/e3WzBNgxLUE7VBbzP8nmE-_9X48cm8-8QCLcB/s72-c/fractal-346127.jpg
Global Journals | Science Innovations & Stories Blog
https://blog.gjsfr.org/2016/05/visualizing-finite-field-of-order-p-2.html
https://blog.gjsfr.org/
http://blog.gjsfr.org/
http://blog.gjsfr.org/2016/05/visualizing-finite-field-of-order-p-2.html
true
1033650636668253683
UTF-8
Not found any posts VIEW ALL Readmore Reply Cancel reply Delete By Home PAGES POSTS View All RECOMMENDED FOR YOU LABEL ARCHIVE SEARCH ALL POSTS Not found any post match with your request Back Home Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sun Mon Tue Wed Thu Fri Sat January February March April May June July August September October November December Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec just now 1 minute ago $$1$$ minutes ago 1 hour ago $$1$$ hours ago Yesterday $$1$$ days ago $$1$$ weeks ago more than 5 weeks ago Followers Follow THIS CONTENT IS PREMIUM Please share to unlock Copy All Code Select All Code All codes were copied to your clipboard Can not copy the codes / texts, please press [CTRL]+[C] (or CMD+C with Mac) to copy