On \((\alpha ,\beta )\)-derivations in \(d\)-algebras (Q2011326)
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scientific article; zbMATH DE number 7140947
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \((\alpha ,\beta )\)-derivations in \(d\)-algebras |
scientific article; zbMATH DE number 7140947 |
Statements
On \((\alpha ,\beta )\)-derivations in \(d\)-algebras (English)
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6 December 2019
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A \(d\)-algebra is a non-empty set \(X\) with a binary multiplication and a fixed element \(0\) such that \(xx=0x=0\) and the implication \(xy=yx=0\rightarrow x=y\) is valid. A map \(g:X\rightarrow X\) is an \((\alpha,\beta)\)-derivation on \(X\) if \(g(xy)=g(x)\alpha(y)\wedge\beta(x)g(y)\) for endomorphisms \(\alpha,\beta\) and \(x\wedge y=y(yx)\). Elementary properties of such derivations are proved.
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\(d\)-algebras
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BCI-algebras
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\((\alpha, \beta )\)-derivations
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