A left ideal is a subset of a ring that is closed under addition and, when multiplied by any element of the ring, the result remains in the subset. This means that for any element 'a' in the left ideal and any element 'r' in the ring, the product 'ra' is also in the left ideal. Left ideals are fundamental in understanding the structure of rings, particularly in the context of representations and C*-algebras.
congrats on reading the definition of Left Ideal. now let's actually learn it.