On some Gelfand-Mazur like theorems in Banach algebras: On some Gelfand-Mazur like theorems in P-normed algebras: Corrigenda

Publisher： Cambridge University Press

E-ISSN： 1755-1633|23|3|479-480

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.23, Iss.3, 1981-06, pp. : 479-480

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Abstract

REMARK 1. In my paper “On some Gelfand-Mazur like theorems in Banach algebras” [2], I stated as Theorem 3.1 the following result: If A is a complex Banach algebra, which is locally finite and if A is an integral domain then A is isomorphic to C. The proof given there is wrong. The mistake occurred when the principal ideal (h) was considered. Certainly (h) is finitely generated as an ideal, but not necessarily as an algebra. However thanks to the following theorem of Heinze [1], the stated Theorem 3.1 of my paper [2] is still correct. Heinze's results states: An associative locally finite algebra which is also an integral domain, over an algebraically closed field is isomorphic to the ground field. The other theorems stated in [2] are correct.