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This question is because of this comment. I would like to know if I should refrain from using $\lhd$ for "is an ideal of" in ring-theoretic questions. Is it common enough, or should I explain what it means? It's standard notation where I study, but I understand it doesn't have to be everywhere.

Also, is there any strong argument for choosing either $\lhd$ or $\triangleleft$? I don't know much about math typesetting, and I've noticed that people can give surprising and convincing arguments for using one symbol and not using another.

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    @user1729 I mean that said notation is used far less commonly in ring theory literature than in group theory literature. In fact, so infrequently that I cannot recall the last time I saw it used.2012-05-22

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I have checked several textbooks (such as Reid's commutative algebra, Dummit's abstract algebra and even Isaac's Algebra) and none of them seem to use the notation you are suggesting. So it doesn't look standard to me.

EDIT: As usual Wiki comes to the rescue! In this wiki page is says that the symbol is used to denote normal subgroups, IDEALS, and the antijoin. So it must be somewhat "standard". Maybe it was popular in the past but not anymore.

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    And according to wiki there seems to be no difference between the two symbols listed.2012-05-23
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I swore I saw this notation somewhere and it took me over an hour to find it.

It's in P.M. Cohn's Introduction to ring theory 2000 ed.

On page 12, he says "One often writes $A \lhd R$ to indicate that $A$ is an ideal of $R$.".

I cannot tell which symbol he used for typesetting.

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    Heh-heh, saying something is often done is one way to convince a reader to do it. That notation is pretty rare in my experience.2012-05-23
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It would be a good idea to define the notation if you use it. It is not standard notation everywhere.

(I don't know which typesetting is preferred.)

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    @scaaahu I have never seen this notation used in semigroup theory either. I was asking about ring-theoretic ideals.2012-05-22