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A note on power values of generalized derivation in prime ring and noncommutative Banach algebras

Shervin Sahebi, Venus Rahmani

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Abstract

Let R be a prime ring with extended centroid C, H a generalized derivation of R and n ⩾ 1 a xed integer. In this paper we study the situations: (1) If ( H(xy)) n = (H(x)) n (H(y)) n for all x;y 2 R; (2) obtain some related result in case R is a noncommutative Banach algebra and H is continuous or spectrally bounded.

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Let R be a prime ring with extended centroid C, H a generalized derivation of R and n ⩾ 1 a xed integer. In this paper we study the situations: (1) If ( H(xy)) n = (H(x)) n (H(y)) n for all x;y 2 R; (2) obtain some related result in case R is a noncommutative Banach algebra and H is continuous or spectrally bounded.

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Available abstract

Let R be a prime ring with extended centroid C, H a generalized derivation of R and n ⩾ 1 a xed integer. In this paper we study the situations: (1) If ( H(xy)) n = (H(x)) n (H(y)) n for all x;y 2 R; (2) obtain some related result in case R is a noncommutative Banach algebra and H is continuous or spectrally bounded.

Key concepts: Noncommutative geometry, Mathematics, Prime ring, Banach algebra, Prime (order theory), Bounded function, Integer (computer science), Ring (chemistry)

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