Rings with a finite set of nonnilpotents

Mohan S. Putcha and Adil Yaqub

International Journal of Mathematics and Mathematical Sciences, 1979, vol. 2, 1-6

Abstract:

Let R be a ring and let N denote the set of nilpotent elements of R . Let n be a nonnegative integer. The ring R is called a θ n -ring if the number of elements in R which are not in N is at most n . The following theorem is proved: If R is a θ n -ring, then R is nil or R is finite. Conversely, if R is a nil ring or a finite ring, then R is a θ n -ring for some n . The proof of this theorem uses the structure theory of rings, beginning with the division ring case, followed by the primitive ring case, and then the semisimple ring case. Finally, the general case is considered.

Date: 1979
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2/509265.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2/509265.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:509265

DOI: 10.1155/S0161171279000120

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().