Abstract
In this paper, the notion of generalized derivations is characterized. Also, the action of these derivations on ideals is investigated and as a consequence, some results involving commutator identities are proved. Further, we explore the commutativity of prime additively inverse semirings in which generalized derivations satisfy certain differential identities. An extension to Posner’s second theorem is also established in the framework of generalized derivations.
Funding statement: The second author also gratefully acknowledges the financial assistance she received from U.G.C., India.
Acknowledgements
The authors are very grateful to the referees for their careful reading of the manuscript and many valuable suggestions.
References
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Articles in the same Issue
- Frontmatter
- On the well-posedness of the Cauchy problem with weight for systems of linear generalized ordinary differential equations with singularities
- On generalized derivations of semirings
- Non-smooth evolution of non-Newtonian flows influenced by thermal effects
- Ground states for fractional Choquard equations with magnetic fields and critical exponents
- A new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics
- Construction of certain new families related to q-Fubini polynomials
- Representation by degenerate Frobenius–Euler polynomials
- Absolute convergence of the Fourier trigonometric series with gaps
- Inverse of Berge’s maximum theorem in locally convex topological vector spaces and its applications
- On the negative order Cesáro summability of double series with respect to block-orthonormal systems
- Finiteness of meromorphic mappings from a complete Kähler manifold into a projective space
Articles in the same Issue
- Frontmatter
- On the well-posedness of the Cauchy problem with weight for systems of linear generalized ordinary differential equations with singularities
- On generalized derivations of semirings
- Non-smooth evolution of non-Newtonian flows influenced by thermal effects
- Ground states for fractional Choquard equations with magnetic fields and critical exponents
- A new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics
- Construction of certain new families related to q-Fubini polynomials
- Representation by degenerate Frobenius–Euler polynomials
- Absolute convergence of the Fourier trigonometric series with gaps
- Inverse of Berge’s maximum theorem in locally convex topological vector spaces and its applications
- On the negative order Cesáro summability of double series with respect to block-orthonormal systems
- Finiteness of meromorphic mappings from a complete Kähler manifold into a projective space