# What does this joke mean?

I saw this written on a blackboard in the math department building the other day:

Gas Law: $PV=nRT$

Ideal Gas Law: $(P)(V)=(n)(R)(T)$

I know the ideal gas law is something from chemistry, but I'm assuming this is meant to be some sort of joke involving math. Any ideas?

• It's simply, in commutative algebra, the ideal generated by a element $a$ is usually denoted $(a)$. – Bernard Dec 13 '15 at 1:54
• And people say we don't have good jokes. Fancy that. – peter a g Dec 13 '15 at 2:46
• I don't like "gassy" jokes so much ... – Hagen von Eitzen Dec 13 '15 at 10:44

In a ring, "$(a)$" is common notation for the principal ideal generated by $a$. (See https://en.wikipedia.org/wiki/Principal_ideal.)
• But if the gas law is the equality $PV=nRT$, then the ideal gas law would be $(PV=nRT)$. The joke doesn't work. – Git Gud Dec 13 '15 at 13:02