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Special Sylvester equations, PI and EP elements in rings with involution

Ruju Zhao,Junchao Wei

JOURNAL OF ALGEBRA AND ITS APPLICATIONS（2023）

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Abstract
In this paper, we study the general solution to certain special Sylvester equations, PI and EP elements in rings with involution. Especially, some practical necessary and sufficient solvability conditions for special Sylvester equations axa dagger a - aa* ya = 0 and aa* x - ya dagger a = c are presented, and expressions of the general solution to these two equations when they are solvable are provided.
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Key words
Special Sylvester equation, general solution, PI element, EP element
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