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Faithfully quadratic rings - a summary of results

M. Dickmann, F. Miraglia (2016)

Banach Center Publications

This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.

Five regular or nearly-regular ternary quadratic forms

William C. Jagy (1996)

Acta Arithmetica

1. Introduction. In a recent article [6], the positive definite ternary quadratic forms that can possibly represent all odd positive integers were found. There are only twenty-three such forms (up to equivalence). Of these, the first nineteen were proven to represent all odd numbers. The next four are listed as "candidates". The aim of the present paper is to show that one of the candidate forms h = x² + 3y² + 11z² + xy + 7yz does represent all odd (positive) integers, and that it is regular in...

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