Taiwanese Journal of Mathematics

MAPS ACTING ON SOME ZERO PRODUCTS

Abstract

Let $R$ be a prime ring with nontrivial idempotents. Assume $\ast$ is an involution of $R$. In this note we characterize the additive map $\delta \colon R \to R$ such that $\delta(x) y^\ast + x \delta(y)^\ast = 0$ whenever $xy^\ast = 0$ and $\phi \colon R \to R$ such that $\phi(x) \phi(y)^\ast = 0$ whenever $xy^\ast = 0$.

Article information

Source
Taiwanese J. Math., Volume 18, Number 1 (2014), 257-264.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706341

Digital Object Identifier
doi:10.11650/tjm.18.2014.2476

Mathematical Reviews number (MathSciNet)
MR3162123

Zentralblatt MATH identifier
1357.16037

Citation

Chen, Hung-Yuan; Liu, Kun-Shan; Mozumder, Muzibur Rahman. MAPS ACTING ON SOME ZERO PRODUCTS. Taiwanese J. Math. 18 (2014), no. 1, 257--264. doi:10.11650/tjm.18.2014.2476. https://projecteuclid.org/euclid.twjm/1499706341

References

• K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with generalized identities, Vol. 196, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker Inc., New York, 1996.
• M. Bre\ptmrs šar, On generalized biderivations and related maps, J. Algebra, 172(3) (1995), 764-786.
• M. A. Chebotar, W.-F. Ke and P.-H. Lee, Maps characterized by action on zero products, Pacific J. Math., 216(2) (2004), 217-228.
• C.-L. Chuang, $*$-differential identities of prime rings with involution, Trans. Amer. Math. Soc., 316(1) (1989), 251-279.
• C.-L. Chuang and T.-K. Lee, Derivations modulo elementary operators, J. Algebra, 338 (2011), 56-70.
• V. K. Kharchenko, Differential identities of prime rings, engl. transl., Algebra and Logic, 17(2) (1978), 155-168.
• C. Lanaki, Conjugates in prime rings, Trans. Amer. Math. Soc., 154 (1971), 185-192.
• T.-K. Lee, Generalized skew derivations characterized by acting on zero products, Pacific J. Math., 216(2) (2004), 293-301.
• G. A. Swain, Maps preserving zeros of $xy^*$, Comm. Algebra, 38(5) (2010), 1613-1620.