Strongly Goldie Dimension

Details Strongly Goldie Dimension Strongly Goldie Dimension

2005-10-09

arxiv.org/abs/math/0510175v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

Let $R$ be an associative ring with identity. A unital right $R$-module $M$ is called strongly finite dimensional if Sup$\{{\rm G.dim} (M/N) | N\leq M\} < +\infty$. Properties of strongly finite dimensional modules are explored. It is also proved that: (1)If $R$ is left $F$-injective and strongly right finite dimensional, then $R$ is left finite dimensional. (2) If $R$ is right $F$-injective, then $R$ is right finite dimensional if and only if $R$ is semilocal. Thus the Faith-Menal conjecture is true if $R$ is strongly right finite dimensional. Some known results are obtained as corollaries.

Affiliated with

Also associated with

No associations

Rating

Strongly Goldie Dimension 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 Strongly Goldie Dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Strongly Goldie Dimension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-146805