Generalized (; )-derivations and Left Ideals in Prime and Semiprime Rings

Asma Ali; Hamidur Rahaman

doi:10.24297/jam.v13i2.6024

Authors

Asma Ali Aligarh Muslim University, Aligarh-202002
Hamidur Rahaman Aligarh Muslim University, Aligarh-202002

DOI:

https://doi.org/10.24297/jam.v13i2.6024

Keywords:

Prime rings, Semiprime rings, Generalized (; )-derivations, (; )- derivations

Abstract

Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! R
be an (; )-derivation. In the present paper we discuss the following situations: (i) F(xoy) = a(xy yx), (ii) F([x; y]) = a(xy yx), (iii) d(x)od(y) = a(xy yx) for
all x; y 2 and a 2 f0; 1;ô€€€1g. Also some related results have been obtained.

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Author Biographies

Asma Ali, Aligarh Muslim University, Aligarh-202002

Department of Mathematics

Hamidur Rahaman, Aligarh Muslim University, Aligarh-202002

Department of Mathematics

References

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