fq-Derivations of G-Algebra
We introduce the notion of fq-derivation as a new derivation of G-algebra. For an endomorphism map f of any G-algebra X, we show that at least one fq-derivation of X exists. Moreover, for such a map, we show that a self-map dqf of X is fq-derivation of X if X is an associative medial G-algebra. For...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2016-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2016/9276096 |
| Summary: | We introduce the notion of fq-derivation as a new derivation of G-algebra. For an endomorphism map f of any G-algebra X, we show that at least one fq-derivation of X exists. Moreover, for such a map, we show that a self-map dqf of X is fq-derivation of X if X is an associative medial G-algebra. For a medial G-algebra X, dqf is fq-derivation of X if dqf is an outside fq-derivation of X. Finally, we show that if f is the identity endomorphism of X then the composition of two fq-derivations of X is a fq-derivation. Moreover, we give a condition to get a commutative composition. |
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| ISSN: | 0161-1712 1687-0425 |