JOURNAL ARTICLE

On a certain functional identity involving inverses in division rings and local rings.

  • Published In: Journal of Algebra & Its Applications, 2025, v. 24, n. 9. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Cezayirlioğlu, Nefise; Demir, Çağrı 3 of 3

Abstract

Let D be a division ring, σ an automorphism of D and u ∈ D a fixed element. We determine the forms of additive maps f , g : D → D satisfying the identity f (x) x − 1 + σ (x) g (x − 1) = u , for every nonzero x ∈ D. We show that f and g are both generalized σ -derivations of D except possibly when σ is the identity automorphism and D is an imperfect field of characteristic 2. We further study the same rational identity in the context of local rings under some mild assumptions. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Algebra & Its Applications. 2025/08, Vol. 24, Issue 9, p1
  • Document Type:Article
  • Subject Area:History
  • Publication Date:2025
  • ISSN:0219-4988
  • DOI:10.1142/S0219498825502202
  • Accession Number:184767200
  • Copyright Statement:Copyright of Journal of Algebra & Its Applications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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