Some results in prime rings involving endomorphisms
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Abdelkarim Boua
,
Abderrahmane Raji
Abstract
In this paper, we generalize some results from [M. Ashraf and S. Ali, On left multipliers and the commutativity of prime rings, Demonstr. Math. 41 2008, 4, 763–771] and present our contribution to the study of endomorphisms. In particular, we prove that a prime ring must be an integral domain if it admits endomorphisms and multipliers satisfying some algebraic identities on non-zero ideals. As a consequence of our main theorems, many known results can either be generalized or deduced. Furthermore, an example is given to show that the necessity of the primeness assumption imposed on the hypotheses of various theorems cannot be unnecessary.
Acknowledgements
The authors would like to thank the referee for the valuable suggestions and comments.
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Some results in prime rings involving endomorphisms
- On the generalized fractional Laplace–Bessel operator
- Smoothness of solutions of differential equations of constant strength in Roumieu spaces
- Rings additively generated by certain periodic elements
- Rings whose clean elements are uniquely strongly clean
- New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications
- On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces
- Characterization of multiplicative Jordan n-higher derivations on unital rings
- The multiplicative Lie algebra on general linear groups
- The optimal control problem for systems of integro-differential equations with finite and infinite horizon
- Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
- Nonlinear mixed Jordan-type derivations on *-algebras
- SG pseudo-differential operators in Dunkl setting
- Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
- The binary products of algebras with genetic realization
-
A relationship between the structure of a quotient ring and
Artikel in diesem Heft
- Frontmatter
- Some results in prime rings involving endomorphisms
- On the generalized fractional Laplace–Bessel operator
- Smoothness of solutions of differential equations of constant strength in Roumieu spaces
- Rings additively generated by certain periodic elements
- Rings whose clean elements are uniquely strongly clean
- New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications
- On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces
- Characterization of multiplicative Jordan n-higher derivations on unital rings
- The multiplicative Lie algebra on general linear groups
- The optimal control problem for systems of integro-differential equations with finite and infinite horizon
- Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
- Nonlinear mixed Jordan-type derivations on *-algebras
- SG pseudo-differential operators in Dunkl setting
- Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
- The binary products of algebras with genetic realization
-
A relationship between the structure of a quotient ring and
