Finding the radical of an algebra of linear transformations

A.M. Cohen; G. Ivanyos; D.B. Wales

doi:10.1016/S0022-4049(97)00010-8

Finding the radical of an algebra of linear transformations

A.M. Cohen, G. Ivanyos, D.B. Wales

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-review

19 Citations (Scopus)

Abstract

We present a method that reduces the problem of computing the radical of a matrix algebra over an arbitrary field to solving systems of semilinear equations. The complexity of the algorithm, measured in the number of arithmetic operations and the total number of the coefficients passed to an oracle for solving semilinear equations, is polynomial. As an application of the technique we present a simple test for isomorphism of semisimple modules.

Original language	English
Pages (from-to)	177-193
Number of pages	17
Journal	Journal of Pure and Applied Algebra
Volume	117-118
DOIs	https://doi.org/10.1016/S0022-4049(97)00010-8
Publication status	Published - 1997

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title = "Finding the radical of an algebra of linear transformations",

abstract = "We present a method that reduces the problem of computing the radical of a matrix algebra over an arbitrary field to solving systems of semilinear equations. The complexity of the algorithm, measured in the number of arithmetic operations and the total number of the coefficients passed to an oracle for solving semilinear equations, is polynomial. As an application of the technique we present a simple test for isomorphism of semisimple modules.",

author = "A.M. Cohen and G. Ivanyos and D.B. Wales",

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AU - Ivanyos, G.

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AB - We present a method that reduces the problem of computing the radical of a matrix algebra over an arbitrary field to solving systems of semilinear equations. The complexity of the algorithm, measured in the number of arithmetic operations and the total number of the coefficients passed to an oracle for solving semilinear equations, is polynomial. As an application of the technique we present a simple test for isomorphism of semisimple modules.

U2 - 10.1016/S0022-4049(97)00010-8

DO - 10.1016/S0022-4049(97)00010-8

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EP - 193

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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