Document Type

Article

Department

Mathematics (HMC)

Publication Date

1953

Abstract

Let R be the ring of entire functions, and let K be the complex field. In an earlier paper [6], the author investigated the ideal structure of R, particular attention being paid to the maximal ideals. In 1946, Schilling [9, Lemma 5] stated that every prime ideal of R is maximal. Recently, I. Kaplansky pointed out to the author (in conversation) that this statement is false, and constructed a non maximal prime ideal of R (see Theorem 1(a), below). The purpose of the present paper is to investigate these nonmaximal prime ideals and their residue class fields. The author is indebted to Prof. Kaplansky for making this investigation possible.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,485.

Publisher pdf, posted with permission.

This article is also available at http://projecteuclid.org/euclid.pjm/1103051253.

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© 1953 Mathematical Sciences Publishers

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