IDENTITIES WITH MULTIPLICATIVE GENERALIZED (α, α)-DERIVATIONS OF SEMIPRIME RINGS

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Sandhu G. S., Ayran A., AYDIN N.

Kragujevac Journal of Mathematics, vol.48, no.3, pp.365-382, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.46793/kgjmat2403.365s
  • Journal Name: Kragujevac Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.365-382
  • Keywords: (α,α)-derivation, (α,α)-derivation, automorphism, multiplicative generalized, Semiprime ring
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

Let R be a semiprime ring and α be an automorphism of R. A mapping F: R → R (not necessarily additive) is called multiplicative generalized (α, α)derivation if there exists a unique (α, α)-derivation d of R such that F(xy) = F(x)α(y) + α(x)d(y) for all x, y ∈ R. In the present paper, we intend to study several algebraic identities involving multiplicative generalized (α, α)-derivations on appropriate subsets of semiprime rings and collect the information about the commutative structure of these rings.