Generalized Jordan derivations of Incidence Algebras
Abstract
For a given ring $\mathfrak{R}$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \mathfrak{R})$ to be the incidence algebra of $X$ over $\mathfrak{R}$. Motivated by a Xiao's result which states that every Jordan derivation of $I(X,\mathfrak{R})$ is a derivation in the case $\mathfrak{R}$ is $2$-torsion free, one proves that each generalized Jordan derivation of $I(X,\mathfrak{R})$ is a generalized derivation provided $\mathfrak{R}$ is $2$-torsion free, getting as a consequence the above mentioned result.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.02189
- arXiv:
- arXiv:1806.02189
- Bibcode:
- 2018arXiv180602189M
- Keywords:
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- Mathematics - Operator Algebras;
- 16W25;
- 47B47
- E-Print:
- 7 pages. arXiv admin note: text overlap with arXiv:1411.6123 by other authors