Direct sums of J -rings and radical rings

Xiuzhan Guo

International Journal of Mathematics and Mathematical Sciences, 1995, vol. 18, 1-4

Abstract:

Let R be a ring, J ( R ) the Jacobson radical of R and P the set of potent elements of R . We prove that if R satisfies ( ∗ ) given x , y in R there exist integers m = m ( x , y ) > 1 and n = n ( x , y ) > 1 such that x m y = x y n and if each x ∈ R is the sum of a potent element and a nilpotent element, then N and P are ideals and R = N ⊕ P . We also prove that if R satisfies ( ∗ ) and if each x ∈ R has a representation in the form x = a + u , where a ∈ P and u ∈ J ( R ) ,then P is an ideal and R = J ( R ) ⊕ P .

Date: 1995
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/18/380630.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/18/380630.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:380630

DOI: 10.1155/S0161171295000664

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 ().