Both in abstract algebra and measure theory is there term ring/algebra, but their definition are different and we can not deduce one from the other, the only requirement in definition they share is that they be closed under two operations: addition and multiplication in abstract algebra while difference and union in measure theory. Why we use the same term for these two different notions in two different branches of mathematics? Is there any connection between them? Thanks!

To be more specific, my intention is to compare "ring in measure theory" with "ring in abstract algebra", not "ring" with "algebra". I use notation "ring/algebra" in the post because the term algebra has the same situation, that is, compare "algebra in measure theory" with "algebra in abstract algebra".

notuse the same term? – Mariano Suárez-Alvarez♦ Apr 27 '10 at 4:29Measure Theorybook have some brief discussion of this? – Yemon Choi Apr 27 '10 at 5:25