On T-Sylvester equations over commutative rings

Sheng Chen; Yunbo Tian

doi:10.1016/j.jfranklin.2014.11.012

On T-Sylvester equations over commutative rings

Sheng Chen
, Yunbo Tian^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

2 Scopus citations

Abstract

In 1994, Wimmer showed the necessary and sufficient conditions for solvability of AX-X∗B=C by means of Roth's criterion. It was shown that the equation over complex fields can be solved if and only if certain block matrices built from A, B and C are congruent. In this paper we extend the result to commutative rings with 2 invertible and show that it also holds for finite sets of matrices over a commutative ring with 2 invertible. We also discuss the solvability of X-AX^TB=C over commutative rings with 2 invertible.

Original language	English
Pages (from-to)	1102-1108
Number of pages	7
Journal	Journal of the Franklin Institute
Volume	353
Issue number	5
DOIs	https://doi.org/10.1016/j.jfranklin.2014.11.012
State	Published - 1 Mar 2016

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10.1016/j.jfranklin.2014.11.012

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title = "On T-Sylvester equations over commutative rings",

abstract = "In 1994, Wimmer showed the necessary and sufficient conditions for solvability of AX-X∗B=C by means of Roth's criterion. It was shown that the equation over complex fields can be solved if and only if certain block matrices built from A, B and C are congruent. In this paper we extend the result to commutative rings with 2 invertible and show that it also holds for finite sets of matrices over a commutative ring with 2 invertible. We also discuss the solvability of X-AXTB=C over commutative rings with 2 invertible.",

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AU - Tian, Yunbo

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AB - In 1994, Wimmer showed the necessary and sufficient conditions for solvability of AX-X∗B=C by means of Roth's criterion. It was shown that the equation over complex fields can be solved if and only if certain block matrices built from A, B and C are congruent. In this paper we extend the result to commutative rings with 2 invertible and show that it also holds for finite sets of matrices over a commutative ring with 2 invertible. We also discuss the solvability of X-AXTB=C over commutative rings with 2 invertible.

UR - https://www.scopus.com/pages/publications/84914170764

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DO - 10.1016/j.jfranklin.2014.11.012

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VL - 353

SP - 1102

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JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

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ER -

On T-Sylvester equations over commutative rings

Abstract

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