Suppose I have an ideal $I = (r, s, t)$. What operations can I apply to the $r$, $s$, and $t$, so that I get an ideal equal to $I$? For example, $(r, s, t) = (r - s, s, t)$. What are the other ones?
Operations on generators of an ideal
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ring-theory
ideals
abstract-algebra
1 Answers
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HINT $\ $ In analogy with change of basis in linear algebra, consider linear transformations of the ideal generators \rm\: (r',s',t') = (r,s,t)\:A\:.\: What kind of matrices $\rm\:A\:$ suffice to preserve the ideal?
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0And there are also non-linear ones. – 2011-11-29