Commutative Algebra I
... By a ring R, we mean a (nonempty) set with two binary operations (addition and
multiplication) satisfying the following conditions:
(1) (R, +) is an abelian group,
(2) multiplication is associative, i.e., for all elements x, y, and z in R, x(yz) =
(xy)z, and distributive over addition, i.e., for all ...