Remarks on symmetric bi-semiderivations and semiprime ideals of rings
Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, cilt.72, sa.2, ss.259-269, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 72 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.47743/anstim.2026.00017
- Dergi Adı: Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica
- Derginin Tarandığı İndeksler: Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO)
- Sayfa Sayıları: ss.259-269
- Anahtar Kelimeler: commutativity, derivations, semiderivations, semiprime ideals, symmetric bi-derivations
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Sivas Cumhuriyet Üniversitesi Adresli: Evet
Özet
The well-known result of E. C. Posner state that a prime ring, if the commutator of each element and its image under a nonzero derivation is central, then the ring is commutative. This result has played a fundamental role in the development of the theory of centralizing mappings on noncommutative rings. Our purpose of this paper is to show this result and its generalizations to symmetric bi-semiderivation in rings without imposing any conditions on the ring, only containing a semiprime ideal. Specifically, we investigate rings that contain a semiprime ideal and prove that centralizing or commuting conditions imposed on symmetric bi-semiderivations force strong structural constraints.