Tom De Medts

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 Name Tom De Medts Member for 2 years Seen 14 hours ago Website Location Belgium Age 33
I am a professor at Ghent University (Belgium). My main research interest is the study of (not necessarily associative) algebras and their connections with other areas, such as group theory and incidence geometry.
 14h comment Name of operations on two vectorsIt's not unlikely that this comes up in tropical geometry (en.wikipedia.org/wiki/Tropical_geometry), where the "product" is the original addition. May29 comment Proving that every term of the sequence is an integer@Barry: I've checked the first $400 \times 400$ entries by computer, and they are all integers. May29 comment Proving that every term of the sequence is an integer(By the way, it's also a little bit confusing that you interchanged rows and columns.) May29 comment Proving that every term of the sequence is an integer@MHMertens: Unfortunately, you did make a calculation mistake. The row $1, 4, 39/2, \dots$ should be $1, 5, 21, 91, \dots$. May27 revised Can repunits be perfect cubes?added 35 characters in body; edited title May27 comment Can repunits be perfect cubes?@Barry: This elementary method doesn't work. In fact, it's not too hard to see that for every positive integer $d$, there exists an integer whose cube ends in at least $d$ digits $1$. (And this number is unique modulo $10^{d+1}$.) May27 accepted Example of a finite group May27 answered Example of a finite group May22 comment Computational Ring Theory Or have a look at Sage on sagemath.org. May7 revised Is Hasse-witt map isomorphism?improved formatting May3 answered The prime number $2$ Mar29 revised P-group with abelian centralzeradded 1173 characters in body Mar29 comment P-group with abelian centralzer@Steve: I am tempted to believe that $C_{p^n} \wr C_p$ might work in general... Mar29 answered P-group with abelian centralzer Mar29 comment P-group with abelian centralzerDo you want such a family for each possible prime $p$, or are you happy with an infinite family for, let's say, $p=2$? Mar13 comment Simple groups analogous to fieldsI agree with Todd. The main observation here is that simple commutative groups and simple commutative rings become rather boring objects (from the point of view of group theory and ring theory, respectively), but simple groups and simple rings (non-commutative ones) are very interesting. Mar13 comment Name for ideal generated by Lie subalgebraI think I would just say "the ideal generated by $\mathfrak{m}$". Feb9 awarded ● Yearling Feb5 comment Skew fields inside quaternion division algebras@Aakumadula: Thanks for your answer! The fact that $(xy - yx)^2$ is a central element is a nice observation. Two questions/comments though: (1) I assume you mean $\deg(D) \geq 3$ instead of $\dim(D) \geq 3$ (where the degree is the square root of the dimension)? (2) I am not assuming $D$ to be finite-dimensional over its center, and the Zariski density argument seems to fail in the infinite-dimensional case. Feb5 comment Skew fields inside quaternion division algebras@Filippo: I use "division algebra" for "skew field which is finite-dimensional over its center". Feb5 comment Skew fields inside quaternion division algebras@Dmitry and Filippo: Indeed, I am not assuming that $D$ is a $k$-algebra (otherwise the result is rather obvious for dimension reasons). Feb4 asked Skew fields inside quaternion division algebras Feb1 comment Is there any need to study Coxeter systems (W,S) with S infinite?I'm not sure whether it answers your question, but Koji Nuida has done quite a bit of research about infinite rank Coxeter groups: www2u.biglobe.ne.jp/~nuida/m/works_e.htm , in particular in his PhD thesis www2u.biglobe.ne.jp/~nuida/m/thesis_text.dvi .