the phrase "a minimal generator" is used. I don't understand what this means in the absence of a specified set of generators. Can anyone explain
commutative-algebra
asked 2011-12-03
user id:20590
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The quotation tells you exactly what the author means by a minimal generator of $M$, and I know no more than that. I don’t know the answer to your question; I was merely offering a couple of definitions of the term in other contexts in hopes that they would suggest a reasonable interpretation in your context. To me they suggest that in your context a minimal generator of an ideal *might* be any element of $I\setminus I(R\setminus\{1\})$ or something similar. (The maximality of $\overline{m}$ in the second definition is clearly not important to the definition.) – 2011-12-03