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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

17 votes
Accepted

When is a power of a nonnegative polynomial a sum of squares?

Motzkin's original proof shows that $x^4y^2 + x^2y^4 + z^6 - a x^2y^2z^2$ is psd and not sos for any $a$ in the interval $(0,3]$. If you take $a = .02$ say, it is reasonably simple, though messy, to s …
Bruce Reznick's user avatar
16 votes
Accepted

Is this Negativstellensatz with uniform denominators known?

Hi. I don't usually read this site, but a friend who does told me about your question. Let me give a couple of answers. The first is that my proof completely doesn't work if $f$ has non-trivial zeros …
Bruce Reznick's user avatar