Idempotent matrix preservers over Boolean algebras

Seok-Zun Song; Kyung-Tae Kang; LeRoy B. Beasley

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J. Korean Math. Soc. 2007; 44(1): 169-178

Printed January 1, 2007

Idempotent matrix preservers over Boolean algebras

Seok-Zun Song, Kyung-Tae Kang, and LeRoy B. Beasley

Cheju National University, Cheju National University, Utah State University

Abstract

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Abstract

We consider the set of $n \times n$ idempotent matrices and we characterize the linear operators that preserve idempotent matrices over Boolean algebras. We also obtain characterizations of linear operators that preserve idempotent matrices over a chain semiring, the nonnegative integers and the nonnegative reals.

Keywords: semiring, idempotent matrix, linear operator

MSC numbers: Primary 15A03, 15A04