20.500.12556/DKUM-93758 On certain functional equation related to derivations In this article, we prove the following result. Let n ≥ 3 be some fixed integer and let R be a prime ring with ≠ + − char R n 1 !2n 2 ( ) ( ) . Suppose there exists an additive mapping D : R → R satisfying the relation 2n−2 D ( x n ) = ( n − 2 ∑ i = 0 ( n − 2 i ) x i D ( x 2 ) x n − 2 − i ) + ( 2 n − 2 − 1 ) ( D ( x ) x n − 1 + x n − 1 D ( x ) ) + n − 2 ∑ i = 1 ( i ∑ k = 2 ( 2 k − 1 − 1 ) ( n − k − 2 i − k ) + n − 1 − i ∑ k = 2 ( 2 k − 1 − 1 ) ( n − k − 2 n − i − k − 1 ) ) x i D ( x ) x n − 1 − i for all x ∈ R. In this case, D is a derivation. This result is related to a classical result of Herstein, which states that any Jordan derivation on a prime ring with char(R) ≠ 2 is a derivation. prime ring semiprime ring derivation Jordan derivation functional equation praštevilski obroči polprimarni obroči izpeljave Jordanova izpeljava funkcionalne enačbe true false true De Gruyter Open Angleški jezik Slovenski jezik Znanstveno delo 2025-07-18 03:07:14 2025-07-18 10:27:09 2025-07-19 03:11:10 0000-00-00 00:00:00 2024 0 0 Str. 1-23 št. 1 Letn. 22 Jan. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2022-02-04 2023-12-03 2024-02-06 517.965 190231299 10.1515/math-2023-0166 2391-5455 https://www.degruyter.com/document/doi/10.1515/math-2023-0166/html 1 8a92d671-6373-11f0-9d87-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193758 On_certain_functional_Marcen_2024.pdf On_certain_functional_Marcen_2024.pdf 1 56DBDBFB4DD1D390B2C992E3390F6D5A 347d8b1c31b9b9a8e7bda511d37f211b5da9065be0a6f2d36499dbd07b0fabd5 72409a29-63b1-11f0-9d87-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193771 Fakulteta za logistiko 0 0 0