A Note on Finitely Generated Z-module and Algebraic Integers

DOI

10.2991/ermm-15.2015.45How to use a DOI?

Keywords

algebraic coding, information system, algebraic integer, monic irreducible polynomial

Abstract

The theory of algebraic integer has its many applications, such as in algebraic coding, cryptology, information system and other fields. The research of algebraic integer can not leave finitely generated module, and the finitely generated module itself be also applied in group theory, ring theory, and some applied science. In this paper, we research the theory of algebraic integer using finitely generated module as tool, we obtained necessary and sufficient condition that an element is algebraic integer, and an intrinsic connects between algebraic number field and finitely generated Z-module.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Lijiang Zeng
PY  - 2015/04
DA  - 2015/04
TI  - A Note on Finitely Generated Z-module and Algebraic Integers
BT  - Proceedings of the 2015 International Conference on Education Reform and Modern Management
PB  - Atlantis Press
SP  - 172
EP  - 174
SN  - 2352-5398
UR  - https://doi.org/10.2991/ermm-15.2015.45
DO  - 10.2991/ermm-15.2015.45
ID  - Zeng2015/04
ER  -