Cyclotomic equations and square properties in rings.

Fine, Benjamin

Displaying similar documents to “Cyclotomic equations and square properties in rings.”

Sums of squares in rings of integers with 2 inverted

Gaël Collinet (2016)

Acta Arithmetica

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We prove that in a ring of S-integers containing 1/2, any totally positive element is a sum of five squares. We also exhibit examples of such rings where some totally positive elements cannot be written as the sum of four squares.

Levels of rings - a survey

Detlev W. Hoffmann (2016)

Banach Center Publications

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Let R be a ring with 1 ≠ 0. The level s(R) of R is the least integer n such that -1 is a sum of n squares in R provided such an integer exists, otherwise one defines the level to be infinite. In this survey, we give an overview on the history and the major results concerning the level of rings and some related questions on sums of squares in rings with finite level. The main focus will be on levels of fields, of simple noncommutative rings, in particular division rings, and of arbitrary...