@article{Dar_Ali_Abbasi_Ayedh_2023, title={Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements}, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6751}, DOI={10.37863/umzh.v75i4.6751}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>UDC 512.5</p> </div> </div> </div> <p>We study the Posner second theorem [Proc. Amer. Math. Soc., <strong>8</strong>, 1093–1100 (1957)] and strong com\-mu\-ta\-tivity preserving problem for symmetric and skew symmetric elements involving generalized derivations on prime rings with involution.<span class="Apple-converted-space">&nbsp;</span>The obtained results cover numerous known theorems.&nbsp;We also provide examples showing that the obtained results hold neither in the case of involution of the first kind, nor in the case where the ring is not prime.</p&gt;}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Dar, N. A. and Ali, S. and Abbasi, A. and Ayedh, M.}, year={2023}, month={May}, pages={455 - 466} }