Prime rings with involution involving left multipliers

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-02-0021

Keywords:

Prime ring, Derivation, Multiplier, Involution, Commutativity

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?]) 2 Z(R) for all x 2 R; (iii) Tn(x ? x?) 2 Z(R) for all x 2 R; (iv) [S(x), T(x?)] 2 Z(R) for all x 2 R; (v) [S(x), T(x?)] - (x ? x?) 2 Z(R) for all x 2 R; (vi) S(x) ? T(x?) 2 Z(R) for all x 2 R; (vii) S(x) ? T(x?) - [x, x?] 2 Z(R) for all x 2 R. The existence of hypotheses in various theorems have been justified by the examples.

Author Biography

Abdelkarim Boua, Sidi Mohammed Ben Abdellah University.

Polydisciplinary Faculty.

References

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Published

2020-04-24

How to Cite

[1]
A. Boua and M. Ashraf, “Prime rings with involution involving left multipliers”, Proyecciones (Antofagasta, On line), vol. 39, no. 2, pp. 341-359, Apr. 2020.

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Section

Artículos