Mathematics – Rings and Algebras
Scientific paper
2010-09-11
Ring and Module theory, Trends in Mathematics, Birkh\"auser Verlag Basel, Switzerland, (2010) 165 - 174
Mathematics
Rings and Algebras
Proceedings of the International Conference on Ring and Module Theory, Ankara, Turkey, August 2008
Scientific paper
We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of $(\alpha, \beta)$-derivation to $(\alpha, \beta)$-higher derivation and demonstrate that a filter of a hereditary torsion theory that is invariant for $\alpha$ and $\beta$ is $(\alpha, \beta)$-higher derivation invariant. As a consequence, any higher derivation can be extended from a module to its module of quotients. Then, we show that any higher derivation extended to a module of quotients extends also to a module of quotients with respect to a larger torsion theory in such a way that these extensions agree. We also demonstrate these results hold for symmetric filters as well. We finish the paper with answers to two questions posed in [L. Va\s, Extending higher derivations to rings and modules of quotients, International Journal of Algebra, 2 (15) (2008), 711--731]. In particular, we present an example of a non-hereditary torsion theory that is not differential.
Papachristou Charalampos
Vas Lia
No associations
LandOfFree
A note on $(α, β)$-higher derivations and their extensions to modules of quotients 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 A note on $(α, β)$-higher derivations and their extensions to modules of quotients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A note on $(α, β)$-higher derivations and their extensions to modules of quotients will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-562940