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Higher Derivations of Finitary Incidence Algebras

  • Ivan Kaygorodov
  • Mykola Khrypchenko
  • Feng Wei
Article
  • 12 Downloads

Abstract

Let P be a partially ordered set, R a commutative unital ring and FI(P,R) the finitary incidence algebra of P over R. We prove that each R-linear higher derivation of FI(P,R) decomposes into the product of an inner higher derivation of FI(P,R) and the higher derivation of FI(P,R) induced by a higher transitive map on the set of segments of P.

Keywords

Finitary incidence algebra Higher derivation Inner higher derivation Higher transitive map 

Mathematics Subject Classification (2010)

Primary 16S50, 16W25 Secondary 16G20, 06A11 

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Notes

Acknowledgments

The authors are grateful to the reviewer whose suggestions helped them to improve the readability of the paper.

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.CMCCUniversidade Federal do ABCSanto AndréBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolisBrazil
  3. 3.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingPeople’s Republic of China

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