# Camilla Vaernes

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# 34 Actions

Feb5   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.
Feb5   accepted  On the equivalence relation in a right Ore domain.
Jul2   revised   Why is multiplication well defined in this ring with the Ore condition?added 13 characters in body
Jul2   revised   Why is multiplication well defined in this ring with the Ore condition?added 457 characters in body
Jul1   asked     Why is multiplication well defined in this ring with the Ore condition?
Jun30  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?
Jun29  revised   On the equivalence relation in a right Ore domain.added 16 characters in body
Jun29  revised   On the equivalence relation in a right Ore domain.edited title
Jun29  asked     On the equivalence relation in a right Ore domain.
Jun29  accepted  Is there a nice way to classify the ideals of the ring of lower triangular matrices?
Jun17  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.
Jun16  awarded   Commentator
Jun16  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?
Jun16  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?
Jun16  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 $$\begin{pmatrix} r & 0 \\ m & s\end{pmatrix}\begin{pmatrix} 0 & 0 \\ 0 & z\end{pmatrix} =\begin{pmatrix} 0 & 0 \\ 0 & sz\end{pmatrix}$$.
Jun16  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?
Jun16  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?
Jun16  asked     Is there a nice way to classify the ideals of the ring of lower triangular matrices?
Jun16  accepted  Kaplansky's theorem of infinitely many right inverses in monoids?
Jun9   comment   Kaplansky's theorem of infinitely many right inverses in monoids?Thanks ymar, this is a nice, concrete example.
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