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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 1 year |
| seen | Feb 5 at 21:00 | |
| stats | profile views | 56 |
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Feb 5 |
comment |
On the equivalence relation in a right Ore domain. Dear rschwieb sorry for my delay! I hadn't logged in for months. Thank you for writing that out. |
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Feb 5 |
accepted | On the equivalence relation in a right Ore domain. |
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Jul 2 |
revised |
Why is multiplication well defined in this ring with the Ore condition? added 13 characters in body |
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Jul 2 |
revised |
Why is multiplication well defined in this ring with the Ore condition? added 457 characters in body |
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Jul 1 |
asked | Why is multiplication well defined in this ring with the Ore condition? |
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Jun 30 |
comment |
On the equivalence relation in a right Ore domain. Thanks rschwieb. I'm using your definition of $\sim$, and I see that $\sim$ is an equivalence relation, and I'm still assuming the common right multiple property. I have addition defined as $a/b+c/d=(ad_1+cb_1)/m$ where $m=bd_1=db_1\neq 0$, and $(a/b)(c/d)=ac_1/db_1$ where $cb_1=bc_1$ and $b_1\neq 0$, but I've struggled and don't know how to show these are well-defined. Do you know how to show that they are? |
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Jun 29 |
revised |
On the equivalence relation in a right Ore domain. added 16 characters in body |
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Jun 29 |
revised |
On the equivalence relation in a right Ore domain. edited title |
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Jun 29 |
asked | On the equivalence relation in a right Ore domain. |
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Jun 29 |
accepted | Is there a nice way to classify the ideals of the ring of lower triangular matrices? |
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Jun 17 |
comment |
Is there a nice way to classify the ideals of the ring of lower triangular matrices? Ok, I think I see where I went wrong, thanks. |
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Jun 16 |
awarded | Commentator |
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Jun 16 |
comment |
Is there a nice way to classify the ideals of the ring of lower triangular matrices? Oh, it just has to be any ideal of $\mathbb{Z}$ also containing $J_1$, right? |
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Jun 16 |
comment |
Is there a nice way to classify the ideals of the ring of lower triangular matrices? So the ideal has form $$\begin{pmatrix} J_2 & 0 \\ ? & J_1\end{pmatrix}$$ for $J_2,J_1$ ideals of $\mathbb{Z}$. How does one describe what goes in the ? place? It has to be an ideal of $\mathbb{Z}$, and also contain $J_1$ I think? |
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Jun 16 |
comment |
Is there a nice way to classify the ideals of the ring of lower triangular matrices? Thanks. I'm curious about what the entries for $M$ should look like for right ideals. Right multiplying I found $$\begin{pmatrix} r & 0 \\ m & s\end{pmatrix}\begin{pmatrix} z & 0 \\ 0 & 0\end{pmatrix} =\begin{pmatrix} rz & 0 \\ mz & 0\end{pmatrix}$$ $$\begin{pmatrix} r & 0 \\ m & s\end{pmatrix}\begin{pmatrix} 0 & 0 \\ z & 0\end{pmatrix} =\begin{pmatrix} 0 & 0 \\ sz & 0\end{pmatrix}$$ and $$\begin{pmatrix} r & 0 \\ m & s\end{pmatrix}\begin{pmatrix} 0 & 0 \\ 0 & z\end{pmatrix} =\begin{pmatrix} 0 & 0 \\ 0 & sz\end{pmatrix}$$. |
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Jun 16 |
comment |
Is there a nice way to classify the ideals of the ring of lower triangular matrices? Are guess my main confusion is, are the ideals of $T$ here just those of form $K_1\oplus K_0\oplus K_2$ where $K_1,K_2$ are ideals of $\mathbb{Z}$, and $K_0$ is a submodule of $\mathbb{Z}$ containing $K_1+K_2$? Or does something change slightly? |
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Jun 16 |
comment |
Is there a nice way to classify the ideals of the ring of lower triangular matrices? Thanks rschwieb. I don't have a copy of that book right now, do you mind explaining even briefly how to interpret the third result you linked to for lower triangular matrices? |
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Jun 16 |
asked | Is there a nice way to classify the ideals of the ring of lower triangular matrices? |
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Jun 16 |
accepted | Kaplansky's theorem of infinitely many right inverses in monoids? |
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Jun 9 |
comment |
Kaplansky's theorem of infinitely many right inverses in monoids? Thanks ymar, this is a nice, concrete example. |
