A note on (α, β)-higher derivations and their extensions to modules of quotients

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of (α, β)-derivation to (α, β)-higher derivation and demonstrate that a filter of a hereditary torsion theory that is invariant for α and β is (α, β)-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. Vaš, 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.

Original languageEnglish (US)
Title of host publicationRing and Module Theory
EditorsToma Albu, Gary F. Birkenmeier, Ali Erdoǧan, Adnan Tercan
PublisherSpringer International Publishing
Number of pages10
ISBN (Print)9783034600064
StatePublished - 2010
Externally publishedYes
EventInternational Conference on Ring and Module Theory, 2008 - Ankara, Turkey
Duration: Aug 18 2008Aug 22 2008

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


OtherInternational Conference on Ring and Module Theory, 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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