This needs not to happen for “”. Rings where “” is commutative, that is, for all , are called commutative rings.
The commutative rings are rings which are more like the fields than other rings are, but there are certain dissimilarities. A field has always a multiplicative inverse for each of its nonzero elements, but the same needs not to be true for a commutative ring. Further, in a commutative ring there may exist zero divisors, i.e. nonzero elements having product zero. Since the ideals of a commutative ring are two-sided (http://planetmath.org/Ideal), the these rings are more comfortable to handle than other rings.
The study of commutative rings is called commutative algebra.
|Date of creation||2013-11-12 18:26:58|
|Last modified on||2013-11-12 18:26:58|
|Last modified by||pahio (2872)|