k-skew Lie products on prime rings with involution

ABSTRACT

Let ℛ be a ring with an involution ∗ and k a positive integer. The k-skew Lie product of a,b∈ℛ is defined by ${}_{\ast }{[a,b]}_k{=}_{\ast }{\left[a{,}_{\ast }{[a,b]}_{k-1}\right]}_1$, where ${}_{\ast }{[a,b]}_0=b$ and ${}_{\ast }{[a,b]}_1=ab-b{a}^{\ast }$. In this paper, some useful properties of the k-skew Lie products on prime *-rings are given. Then, as an application of these results, k-skew commuting additive maps on prime *-rings are characterized.

KEYWORDS:

• k-commuting maps
• k-skew Lie products
• skew Lie products
• rings with involution

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W10
• 47B47

Acknowledgements

The authors wish to give their many thanks to the anonymous referee(s) for helpful comments and suggestions that improved the main results in the original manuscript.

This work is partially supported by National Natural Science Foundation of China (11671006), Outstanding Youth Foundation of Shanxi and Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi.