# Question on Ring .Help Please!

1. Apr 24, 2012

### woundedtiger4

Given any non-empty systems of sets S, there is a unique ring P containing S and contained in every ring containing S. The ring P is called the minimal ring generated by the system S & can be denoted as R(S).
Question: what does mean by "there is a unique ring P containing S", does it mean that P is in S ? if I am wrong then is P a maximal set of S?

2. Apr 24, 2012

### sunjin09

It means that S$\subset$P, i.e., S is a set of sets, and P is a RING OF SETS, which contains every element of S as its element (and more, in general). This ring P is said to be generated by the set S, since it is created by adding (symmetric difference) and multiplying (intersection) elements of S, and collecting all the possible outcomes.

3. Apr 25, 2012