A Study on Characteristic of Rings

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-1
Year of Publication : 2021
Authors : Laxman Saha
  10.14445/22315373/IJMTT-V67I1P510

MLA

MLA Style: Laxman Saha "A Study on Characteristic of Rings" International Journal of Mathematics Trends and Technology 67.1 (2021):66-69. 

APA Style: Laxman Saha(2021). A Study on Characteristic of Rings International Journal of Mathematics Trends and Technology, 66-69.

Abstract
The characteristic of a ring R, denoted by ψ(R), is the smallest positive integer n such that nr =0 for all r ε 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.

Reference

[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).

Keywords : Group, Ring, Characteristic.