A Study on Characteristic of Rings

Laxman Saha

doi:https://doi.org/10.14445/22315373/IJMTT-V67I1P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 1 | Year 2021 | Article Id. IJMTT-V67I1P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I1P510

A Study on Characteristic of Rings

Laxman Saha

Citation :

Laxman Saha, "A Study on Characteristic of Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 1, pp. 66-69, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I1P510

Abstract

The characteristic of a ring 𝑅, denoted by 𝛹(𝑅), is the smallest positive integer n such that 𝑛𝑟 = 0 for all 𝑟 ∈ 𝑅. If no such integer exists, we say that R has characteristic 0. In this article, the characteristic of a ring (𝑅, +, . ) is presented in terms of the order of the elements in the commutative group (𝑅, +). 𝐴𝑙𝑠𝑜 𝑖𝑡 has been shown that the prime generators of 𝑂(𝑅) and 𝛹(𝑅) are same. This article also gives a relationship among 𝛹(𝑅),𝛹(𝐼) and 𝛹(𝑅/𝐼) for any ring 𝑅 and any ideal 𝐼 of 𝑅.

Keywords

Group, Ring, Characteristic

References

[1] D.S. Dummit, and R.M. Foote, Abstract Algebra, Wiley India Pvt. Ltd., 2017.
[2] Kleiner, The Genesis of the Abstract Ring Concept, American Mathematical Monthly. 103(1996) 417-424.
[3] G. Birkhoff, and S.M. Lane, A Survey of Modern Algebra, 5th 2d,(1996).