The ideals of an ideal extension

Details The ideals of an ideal extension The ideals of an ideal extension

2009-09-02

arxiv.org/abs/0909.0440v1

J. Algebra Appl. 9 (2010) 407-431

Mathematics

Rings and Algebras

23 pages

Scientific paper

10.1142/S0219498810003999

Given a unital associative ring S and a subring R, we say that S is an ideal (or Dorroh) extension of R if for some ideal I of S, S = R + I, where the sum is direct. In this note we investigate the ideal structure of an arbitrary ideal extension of an arbitrary ring R. In particular, we describe the Jacobson and upper nil radicals of such a ring, in terms of the Jacobson and upper nil radicals of R, and we determine when such a ring is prime and when it is semiprime. We also classify all the prime and maximal ideals of an ideal extension S of R, under certain assumptions on the ideal I. These are generalizations of earlier results in the literature.

Affiliated with

Also associated with

No associations

Rating

The ideals of an ideal extension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The ideals of an ideal extension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The ideals of an ideal extension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-12701