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Higher Derivations of Finitary Incidence Algebras

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. CMCC, Universidade Federal do ABC, Santo André, Brazil

    Ivan Kaygorodov

  2. Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Reitor João David Ferreira Lima, Florianópolis, 88040–900, Brazil

    Mykola Khrypchenko

  3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Feng Wei

Authors
  1. Ivan Kaygorodov
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  2. Mykola Khrypchenko
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  3. Feng Wei
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Corresponding author

Correspondence to Ivan Kaygorodov.

Additional information

Presented by: Jon F. Carlson

This work is partially supported by the Training Program of International Exchange and Cooperation of the Beijing Institute of Technology and RFBR 17-01-00258. The authors would like to thank the International Affair Office of Beijing Institute of Technology for its kind consideration and warm help.

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Kaygorodov, I., Khrypchenko, M. & Wei, F. Higher Derivations of Finitary Incidence Algebras. Algebr Represent Theor 22, 1331–1341 (2019). https://doi.org/10.1007/s10468-018-9822-4

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  • DOI: https://doi.org/10.1007/s10468-018-9822-4

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