Prime rings with involution involving left multipliers
Abstract Let R be a prime ring of characteristic different from 2 with involution ’∗’ of the second kind and n ≥ 1 be a fixed positive integer. In the present paper it is shown that if R admits nonzero left multipliers S and T , then the following conditions a...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200341 |
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| Sumario: | Abstract Let R be a prime ring of characteristic different from 2 with involution ’∗’ of the second kind and n ≥ 1 be a fixed positive integer. In the present paper it is shown that if R admits nonzero left multipliers S and T , then the following conditions are equivalent: (i)R is commutative, (ii) Tn([x, x∗]) ∈ Z(R) for all x ∈ R; (iii) Tn(x ◦ x∗) ∈ Z(R) for all x ∈ R; (iv) [S(x), T (x∗)] ∈ Z(R) for all x ∈ R; (v) [S(x), T (x∗)] − (x ◦ x∗) ∈ Z(R) for all x ∈ R; (vi) S(x) ◦ T (x∗) ∈ Z(R) for all x ∈ R; (vii) S(x) ◦ T (x∗) − [x, x∗] ∈ Z(R) for all x ∈ R. The existence of hypotheses in various theorems have been justified by the examples. |
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