On a characterization of commutativity for prime rings via endomorphisms
DOI :
https://doi.org/10.5269/bspm.50592Résumé
Our aim in the present paper is to introduce new classes of endomorphisms and study their connection with commutativity of prime rings with involution of the second kind. Furthermore, we provide examples to show that the various restrictions imposed in the hypotheses of our theorems are not superfluous.
Références
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2. Bell H. E. and Daif M. N., Center-like subsets in rings with derivations or epimorphisms, Bull. Iranian Math. Soc. 42 4, 873-878, (2016).
3. Deng Q. and Ashraf M., On strong commutativity preserving mappings, Results Math. 30 3-4, 259-263, (1996). https://doi.org/10.1007/BF03322194
4. Khan A. N. and Ali S., Involution on prime rings with endomorphisms, AIMS Mathematics 5 4, 3274-3283, (2020). https://doi.org/10.3934/math.2020210
5. Lanski C., Differential identities, Lie ideals and Posner's theorems, Pacific J. Math. 134 2, 275-297, (1988). https://doi.org/10.2140/pjm.1988.134.275
6. Lee P. H. and Lee T. K., On derivations of prime rings, Chinese J. Math. 9 2, 107-110, (1981).
7. Mamouni A., Oukhtite L. and El Mir H., New classes of endomorphisms and some classification theorems, Comm. Alg. https://doi.org/10.1080/00927872.2019.1632330
8. Nejjar B., Kacha A., Mamouni A. and Oukhtite L., Commutativity theorems in rings with involution, Comm. Alg. 45 2, 698-708, (2017). https://doi.org/10.1080/00927872.2016.1172629
9. Posner E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8 1093-1100, (1957). https://doi.org/10.1090/S0002-9939-1957-0095863-0
2. Bell H. E. and Daif M. N., Center-like subsets in rings with derivations or epimorphisms, Bull. Iranian Math. Soc. 42 4, 873-878, (2016).
3. Deng Q. and Ashraf M., On strong commutativity preserving mappings, Results Math. 30 3-4, 259-263, (1996). https://doi.org/10.1007/BF03322194
4. Khan A. N. and Ali S., Involution on prime rings with endomorphisms, AIMS Mathematics 5 4, 3274-3283, (2020). https://doi.org/10.3934/math.2020210
5. Lanski C., Differential identities, Lie ideals and Posner's theorems, Pacific J. Math. 134 2, 275-297, (1988). https://doi.org/10.2140/pjm.1988.134.275
6. Lee P. H. and Lee T. K., On derivations of prime rings, Chinese J. Math. 9 2, 107-110, (1981).
7. Mamouni A., Oukhtite L. and El Mir H., New classes of endomorphisms and some classification theorems, Comm. Alg. https://doi.org/10.1080/00927872.2019.1632330
8. Nejjar B., Kacha A., Mamouni A. and Oukhtite L., Commutativity theorems in rings with involution, Comm. Alg. 45 2, 698-708, (2017). https://doi.org/10.1080/00927872.2016.1172629
9. Posner E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8 1093-1100, (1957). https://doi.org/10.1090/S0002-9939-1957-0095863-0
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2022-02-07
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