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.