On symmetric bi-derivations acting upon prime ideals in any rings - Sögütcü, Emine Koç; Gölbaşı, Öznur; Dhara, Basudeb (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.5 Let R be a ring, P be a prime ideal of R, I be a nonzero ideal of R such that PI, D_1, D_2, D_3R× R→ R be symmetric bi-derivations, and d_1, d_2, and d_3 be the traces of D_1,D_2, and D_3 respectively. We study the following conditions: (i) [d_1(x),x]P, (ii) d_1(x)° xP, (iii) D_1(d_2(x),x)P, (iv) d_1(d_2(x))± d_3(x)P, and (v) d_1(x)d_2(x)P for all x,yI.