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Commutativity for a Certain Class of Rings
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Hamza A. S. Abujabal
Published/Copyright:
February 23, 2010
Abstract
We discuss the commutativity of certain rings with unity 1 and one-sided s-unital rings under each of the following conditions: xr[xs, y] = ±[x, yt]xn, xr[xs, y] = ±xn[x, yt], xr[xs, y] = ±[x, yt]ym, and xr[xs, y] = ±ym[x, yt], where r, n, and m are non-negative integers and t > 1, s are positive integers such that either s, t are relatively prime or s[x, y] = 0 implies [x, y] = 0. Further, we improve the result of [Jacobson, Structure of rings, Colloq. Publ., 1964, Theorem 3] and reprove several recent results.
Received: 1994-04-19
Revised: 1994-11-02
Published Online: 2010-02-23
Published in Print: 1996-February
© 1996 Plenum Publishing Corporation
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- Partial Averaging for Impulsive Differential Equations with Supremum
- An Algebraic Model of Fibration with the Fiber K(π, n)-Space
- On the Uniqueness of Maximal Functions
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Articles in the same Issue
- Commutativity for a Certain Class of Rings
- Partial Averaging for Impulsive Differential Equations with Supremum
- An Algebraic Model of Fibration with the Fiber K(π, n)-Space
- On the Uniqueness of Maximal Functions
- On the Solvability of a Darboux Type Non-Characteristic Spatial Problem for the Wave Equation
- Littlewood–Paley Operators on the Generalized Lipschitz Spaces
- On Strong Maximal Operators Corresponding to Different Frames
- Complexity of the Decidability of One Class of Formulas in Quantifier-Free Set Theory with a Set-Union Operator
