Idempotent matrices over a duo ring |
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| Author |
a.bilous1610@gmail.com
Institute for Applied Problems of Mechanics and Mathematics,
Lviv, Ukraine
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| Abstract |
In the present paper, we study diagonability of matrices over a duo ring. We prove that an
idempotent matrix over such a ring is diagonalizable under a similarity transformation.
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| Keywords |
PT ring; duo ring; idempotent matrix; diagonalization
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| DOI |
doi:10.30970/ms.52.2.133-137
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| Reference |
1. Foster A. Maximal idempotent sets in a ring with unit// Duke Mathematical Journal. – 1946. – V.13, ¹2.
– P. 247–258.
2. Laksov D. Diagonalization of matrices over rings// Journal of Algebra. – 2013. – V.376. – P. 123–138. 3. Richter R.B., Wardlaw W.P. Diagonalization over commutative rings// The American Mathematical Monthly. – 1990. – V.97, ¹3. – P. 223–227. 4. Steger A. Diagonability of idempotent matrices// Pac. J. Math. – 1966. – V.19, ¹3. – P. 535–542. 5. Steger A. Elementary factorization in $\pi$-regular rings// Canad. J. Math., – 1966. – V.18. – P. 307–313. 6. Shchedryk V.P. Factorization of matrices over elementary divisor rings. – Lviv: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the NAS of Ukraine. – 2017. – 304 p. 7. Tan Y.J. Diagonability of matrices over commutative semirings, Linear and Multilinear Algebra. – 2018. 8. Zabavsky B.V. Diagonal reduction of matrices over rings// Mathematical Studies, Monograph Series, – 2012. – V.16. – 251p. |
| Pages |
133-137
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| Volume |
52
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| Issue |
2
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| Year |
2019
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| Journal |
Matematychni Studii
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| Full text of paper | |
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