Some additive combinatorics problems in matrix rings

R Ferguson; Corneliu Hoffman; F Luca; A Ostafe; IE Shparlinski

doi:10.1007/s13163-010-0029-4

Some additive combinatorics problems in matrix rings

R Ferguson, Corneliu Hoffman, F Luca, A Ostafe, IE Shparlinski

Mathematics

Research output: Contribution to journal › Article

9 Citations (Scopus)

Abstract

We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.

Original language	English
Pages (from-to)	501-513
Number of pages	13
Journal	Revista Matematica Complutense
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s13163-010-0029-4
Publication status	Published - 1 Jul 2010

Keywords

Matrices
Additive combinatorics
Finite fields

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10.1007/s13163-010-0029-4

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title = "Some additive combinatorics problems in matrix rings",

abstract = "We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.",

keywords = "Matrices, Additive combinatorics, Finite fields",

author = "R Ferguson and Corneliu Hoffman and F Luca and A Ostafe and IE Shparlinski",

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AU - Ferguson, R

AU - Hoffman, Corneliu

AU - Luca, F

AU - Ostafe, A

AU - Shparlinski, IE

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Y1 - 2010/7/1

N2 - We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.

AB - We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.

KW - Matrices

KW - Additive combinatorics

KW - Finite fields

U2 - 10.1007/s13163-010-0029-4

DO - 10.1007/s13163-010-0029-4

M3 - Article

VL - 23

SP - 501

EP - 513

JO - Revista Matematica Complutense

JF - Revista Matematica Complutense

IS - 2

ER -

Some additive combinatorics problems in matrix rings

Abstract

Keywords

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