Higher Derivations of Finitary Incidence Algebras

Ivan Kaygorodov; Mykola Khrypchenko; Feng Wei

doi:10.1007/s10468-018-9822-4

Higher Derivations of Finitary Incidence Algebras

Ivan Kaygorodov^*, Mykola Khrypchenko, Feng Wei

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1331-1341
Number of pages	11
Journal	Algebras and Representation Theory
Volume	22
Issue number	6
DOIs	https://doi.org/10.1007/s10468-018-9822-4
Publication status	Published - 1 Dec 2019

Keywords

Finitary incidence algebra
Higher derivation
Higher transitive map
Inner higher derivation

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10.1007/s10468-018-9822-4

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Kaygorodov, I., Khrypchenko, M., & Wei, F. (2019). Higher Derivations of Finitary Incidence Algebras. Algebras and Representation Theory, 22(6), 1331-1341. https://doi.org/10.1007/s10468-018-9822-4

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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.",

keywords = "Finitary incidence algebra, Higher derivation, Higher transitive map, Inner higher derivation",

author = "Ivan Kaygorodov and Mykola Khrypchenko and Feng Wei",

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AU - Kaygorodov, Ivan

AU - Khrypchenko, Mykola

AU - Wei, Feng

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N2 - 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.

AB - 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.

KW - Finitary incidence algebra

KW - Higher derivation

KW - Higher transitive map

KW - Inner higher derivation

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ER -

Higher Derivations of Finitary Incidence Algebras

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Keywords

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