On n-skew Lie Products on Prime Rings with Involution
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Let R be a ∗-ring and n ≥ 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on ∗-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution ′ ∗ ′ such that ∗[x, d(x)]n ∈ Z(R) for all x ∈ R (for n = 1, 2), where d : R → R is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.
Abstract
Let R be a ∗-ring and n ≥ 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on ∗-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution ′ ∗ ′ such that ∗[x, d(x)]n ∈ Z(R) for all x ∈ R (for n = 1, 2), where d : R → R is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.
참고문헌 (5)
- S. Ali, "On ∗-centralizing mappings in rings with involution", Georgain Math. J, 21(1), pp.25~28 (2014)
- I. N. Herstein, "Ring with Involution" (1976), University of Chicago Press
- J. Hou, "Strong 2-skew commutativity preserving maps on prime rings with involution", Bull. Malays. Math. Sci. Soc, 42(1), pp.33~49 (2019)
- E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)
- X. Qi, "k-skew Lie products on prime rings with involution", Comm. Algebra, 46(3), pp.1001~1010 (2018)