Timeline for Rings $R$ such that every [regular] square matrix with entries in $R$ is equivalent to an upper triangular matrix
Current License: CC BY-SA 4.0
9 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| May 24, 2020 at 18:38 | comment | added | Badam Baplan | @Luc Guyot I agree, what I wrote is really a long comment that answers a question somewhere between (1) and the later edit, which asks for sufficiently general conditions. I'd also be interested to know what trigonal reduction of $2 \times 2$ entails for a ring. I will think on it. Even for domains, intuitively feels like a much weaker property than f.g. ideals. | |
| May 24, 2020 at 11:04 | history | edited | Luc Guyot | CC BY-SA 4.0 |
Fixes few typos: wrong date (1948 --> 1949), "is either ... or ..." where or-clause is not an adjective/attribute.
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| May 24, 2020 at 9:29 | comment | added | Luc Guyot | There is still one thing that I find very unsatisfactory with K-Hermite rings: I still ignore whether trigonal reduction of every $2 \times 2$ matrices (the topic of this question) implies trigonal reduction of every $1 \times 2$. It might not be the case. Determining the ring with trigonal reduction of $2 \times 2$ matrices would be an even more on-topic answer. (Mohan's answer is a step forward in this direction.) | |
| May 24, 2020 at 7:40 | vote | accept | Salvo Tringali | ||
| May 23, 2020 at 23:44 | history | edited | Badam Baplan | CC BY-SA 4.0 |
added 1469 characters in body
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| May 23, 2020 at 23:27 | comment | added | Badam Baplan | @YCor A diagonal matrix is just defined as a matrix that is zero off of the main diagonal. That's a reasonable question though. | |
| May 23, 2020 at 23:24 | comment | added | YCor | How can a $1\times 2$ matrix (i.e., non-square) matrix be equivalent to a diagonal (thus square) one? | |
| May 23, 2020 at 19:01 | history | answered | Badam Baplan | CC BY-SA 4.0 |