ScholarLens Back to search
1936•Transactions of the American Mathematical SocietyRequires access

On Ideals in a Quaternion Algebra and the Representation of Integers by Hermitian Forms

Claiborne G. Latimer

Open publisher page 1 citations

Abstract

The statement "there is a one-to-one correspondence • • ■ " in lines 8, 9, p. 442, Tr. is false.There is a correspondence but it is not one-to-one.For if the transformation (8) of Tr. is an automorph of/, then/ corresponds to the bases an, on and fi, ft.This error does not affect the validity of any subsequent proof or theorem.* The condition \ki,-\ =1 and (7) imply that (ka) is the matrix of an automorph of/.If j^O, | kij\ = 1 and the first pair of (7) imply the second pair.

About this research paper

What this paper is about

The statement "there is a one-to-one correspondence • • ■ " in lines 8, 9, p. 442, Tr. is false.There is a correspondence but it is not one-to-one.For if the transformation (8) of Tr. is an automorph of/, then/ corresponds to the bases an, on and fi, ft.This error does not affect the validity of any subsequent proof or theorem.* The condition \ki,-\ =1 and (7) imply that (ka) is the matrix of an automorph of/.If j^O, | kij\ = 1 and the first pair of (7) imply the second pair.

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

The statement "there is a one-to-one correspondence • • ■ " in lines 8, 9, p. 442, Tr. is false.There is a correspondence but it is not one-to-one.For if the transformation (8) of Tr. is an automorph of/, then/ corresponds to the bases an, on and fi, ft.This error does not affect the validity of any subsequent proof or theorem.* The condition \ki,-\ =1 and (7) imply that (ka) is the matrix of an automorph of/.If j^O, | kij\ = 1 and the first pair of (7) imply the second pair.

Key concepts: Mathematics, Quaternion, Hermitian matrix, Algebra over a field, Representation (politics), Quaternion algebra, Pure mathematics, Division algebra

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On Ideals in a Quaternion Algebra and the Representation of Integers by Hermitian Forms — Research Paper | ScholarLens