Higher levels of
ℤ/plℤ and period equations

Becker, Eberhard; Canales, Mónica

doi:10.1007/s002290050183

Cited by 3 publications

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References 4 publications

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“…The ps n of commutative rings is considered in [14], [4] and [3]. The ps n of a commutative ring is the number of terms in the shortest representation of −1 as a sum of n-th powers.…”

Section: Definitions and Elementary Examplesmentioning

confidence: 99%

Higher Product Levels of Noncommutative Rings

Cimpric

2001

Communications in Algebra

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The aim of this paper is to introduce the notion of the n-th product level ps n of an associative unital ring and study its properties. Our main results are that every Noetherian ring A with ps n (A) < ∞ for some n ∈ IN has ps nl (A) < ∞ for every odd number l (Theorem 8) and that for every even n ∈ IN there exists a skew-field D with ps n (D) = 1 and ps 2n (D) = ∞ (Theorem 9). This is in a sharp contrast with the commutative case. Namely, by Proposition 4.6 in [4], for every commutative unital ring R with ps 2 (R) < ∞ we have that ps n (R) < ∞ for every n ∈ IN.

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“…The ps n of commutative rings is considered in [14], [4] and [3]. The ps n of a commutative ring is the number of terms in the shortest representation of −1 as a sum of n-th powers.…”

Section: Definitions and Elementary Examplesmentioning

confidence: 99%

Higher Product Levels of Noncommutative Rings

Cimpric

2001

Communications in Algebra

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“…The study of s n (F ) was initiated by J.-P. Joly in [9] and continued by E. Becker in a series of papers (e.g. [2], [3]). The case n = 2 is classical, see [14].…”

Section: Introductionmentioning

confidence: 99%

A Variant of Higher Product Levels of Integral Domains and *-Domains

Cimpric

2005

Communications in Algebra

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Abstract. For every domain R and every even integer n we define ms n (R) (resp. ps n (R)) as the smallest number k such that 0 is a sum of k + 1 products (resp. permuted products) of n-th powers of nonzero elements from R. There are many results about ps n in the literature but nothing is known about ms n .We prove two results about ms n of twisted Laurent series rings R ((x, ω)). The first result is that if ms 2 (R) = ∞ and ω has order n/2 in Aut(R), then ms n (R((x, ω))) = ∞. The second result is that there exist R and ω such that ms n (R((x, ω))) = ∞ and ps n (R ((x, ω)Finally, we define ms n and ps n of a domain R with involution. For a certain involution on R ((x, ω)), we prove analogues of the first and the second result.

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u-Invariants for forms of higher degree

Pumplün

2009

Expositiones Mathematicae

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Higher levels of ℤ/plℤ and period equations

Cited by 3 publications

References 4 publications

Higher Product Levels of Noncommutative Rings

Higher Product Levels of Noncommutative Rings

A Variant of Higher Product Levels of Integral Domains and *-Domains

u-Invariants for forms of higher degree

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