A note about two properties of matrix rings

A. A. Klein

doi:10.1007/BF02771556

A note about two properties of matrix rings

A. A. Klein^*

^*Corresponding author for this work

School of Mathematical Sciences

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

2 Scopus citations

Abstract

We show that there exists for each m≧2 a (non-commutative) integral domain R with a nilpotent matrix C ∈R_m whose order of nilpotency is greater than m, and any A ∈R_m with a right (or a left) inverse is invertible.

Original language	English
Pages (from-to)	90-92
Number of pages	3
Journal	Israel Journal of Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/BF02771556
State	Published - Mar 1970

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abstract = "We show that there exists for each m≧2 a (non-commutative) integral domain R with a nilpotent matrix C ∈R m whose order of nilpotency is greater than m, and any A ∈R m with a right (or a left) inverse is invertible.",

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A note about two properties of matrix rings

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