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

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

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Abstract

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
Pages165-174
Number of pages10
ISBN (Print)9783034600064
DOIs
StatePublished - 2010
EventInternational Conference on Ring and Module Theory, 2008 - Ankara, Turkey
Duration: Aug 18 2008Aug 22 2008

Publication series

NameTrends in Mathematics
Volume50
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Other

OtherInternational Conference on Ring and Module Theory, 2008
CountryTurkey
CityAnkara
Period8/18/088/22/08

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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