jacobson radical造句

So, for commutative rings, the nilradical is contained in the Jacobson radical.
Lifting is most important when, the Jacobson radical of " R ".
The Jacobson radical of a ring has various internal and external characterizations.
If " R " is commutative, the Jacobson radical always contains the nilradical.
As with other center of the ring are also in the Jacobson radical.
It's difficult to find jacobson radical in a sentence. 用jacobson radical造句挺难的

The Jacobson radical is very similar to the nilradical in an intuitive sense.
The only idempotent contained in the Jacobson radical of a ring is 0.
It is contained in, but in general not equal to, the ring's Jacobson radical.
Elements of the Jacobson radical and nilradical can be therefore seen as generalizations of 0.
*PM : properties of the Jacobson radical, id = 3152-- WP guess : properties of the Jacobson radical-- Status:
*PM : properties of the Jacobson radical, id = 3152-- WP guess : properties of the Jacobson radical-- Status:
In the next few years several other radicals were discovered, of which the most important example is the Jacobson radical.
From the above properties, a ring is semisimple if and only if it is Artinian and its Jacobson radical is zero.
If these properties hold, then the unique maximal left ideal coincides with the unique maximal right ideal and with the ring's Jacobson radical.
*PM : proof of characterizations of the Jacobson radical, id = 3137-- WP guess : proof of characterizations of the Jacobson radical-- Status:

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