1
vote
1answer
141 views

How many ways are there to represent a monomial order, defined by $>$, by term order via matrices?

During the lecture, my professor brought up the list of project ideas to work on. One of the ideas I am interested and currently working on is term order via matrices. That is: I need to find the ...
-3
votes
1answer
105 views

Computational commutative algebra: term orders [closed]

Is it true that in $k[x,y]$ the monomial orders deglex and degrevlex are same? Here, deglex and degrevlex are defined as in Sage.
0
votes
1answer
63 views

On the alphabetical order of monomial

I found this definition of alphabetical order for monomials in $k[x_1,\ldots,x_n]$. We say that $x_1^{a_1}\cdots x_n^{a_n}>x_1^{b_1}\cdots x_n^{b_n}$ if for the least $i$ such that $a_i\neq b_i$ we ...
4
votes
1answer
69 views

Is the semigroup generated by wellordered positive set wellordered?

Let $(A,\leq)$ be a totally ordered abelian group, and $\Gamma\subseteq A$ be a set of nonnegative elements, such that it is wellordered by $\leq$. Is it true then that the semigroup $S$ generated by ...
11
votes
3answers
581 views

Examples of rings with ideal lattice isomorphic to $M_3$, $N_5$

In thinking about this recent question, I was reading about distributive lattices, and the Wikipedia article includes a very interesting characterization: A lattice is distributive if and only if ...
3
votes
2answers
275 views

Totally ordered abelian group

Let $\Gamma$ be a totally ordered abelian group (written additively), and let $K$ be a field. A valuation of $K$ with values in $\Gamma$ is a mapping $v:K^* \to \Gamma$ such that $1)$ ...