(b) if , and , then ;
(c) if is a two-sided ideal of and , then as well;
(d) if is a left ideal of and , then as well;
(e) if is a right ideal of and , then as well.
Here is the product of ideals .
The ring itself satisfies all of these conditions (including being expressed as an intersection of an empty family of prime ideals) and is thus semiprime.
Note that an ideal of is semiprime if and only if the quotient ring is a semiprime ring.
|Date of creation||2013-03-22 12:01:23|
|Last modified on||2013-03-22 12:01:23|
|Last modified by||antizeus (11)|