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In commutative algebra, there seem to be two rather different notational conventions for ideals: either $I,J, \dots$ or $\mathfrak{a}, \mathfrak{b}, \dots$.

By itself, it is hardly surprising - after all, lots of other notations vary from source to source. I have, however, come across both conventions in a single script or article on many occasions. And the difference is rather striking: different letter is used, different case, different font...

I find this rather surprising and a little confusing, since usually a single convention is used within a piece of writing. I would very much appreciate any information on where such notational complication comes from. Is one of these conventions preferable (in some circumstances)?

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    Ideally, $\mathfrak{i}$,2012-09-21

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Since Bourbaki in His Commutative Algebra and His prophets Dieudonné and Grothendieck in EGA use Fraktur, you have no choice but to do the same.
I shudder to think of the fate befalling heretics and miscreants who would incur His ire by using Latin letters.

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    Thanks, Feanor: I'm glad you agree with the answer.2012-09-22
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If you are clear when you define things, and use the same convention consistently, and you don't go out of your way to make the notation ridiculous, nobody cares.

I think whatever you pick (within reason) you'll do fine.

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    I won't, I also dislike it. In particular, it is not even obvious which letter it represents unless you know it in advance (it could well be U as well as A, or even M).2012-09-22