Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian

Details Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian

2010-01-23

arxiv.org/abs/1001.4132v1

Mathematics

Rings and Algebras

A Para\^itre Glasgow Mathematical Journal

Scientific paper

R is called a right WV -ring if each simple right R-module is injective relative to proper cyclics. If R is a right WV -ring, then R is right uniform or a right V -ring. It is shown that for a right WV-ring R, R is right noetherian if and only if each right cyclic module is a direct sum of a projective module and a CS or noetherian module. For a finitely generated module M with projective socle over a V -ring R such that every subfactor of M is a direct sum of a projective module and a CS or noetherian module, we show M = X \oplus T, where X is semisimple and T is noetherian with zero socle. In the case that M = R, we get R = S \oplus T, where S is a semisimple artinian ring, and T is a direct sum of right noetherian simple rings with zero socle. In addition, if R is a von Neumann regular ring, then it is semisimple artinian.

Affiliated with

Also associated with

No associations

Rating

Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian 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 Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-514881