radical of a ring वाक्य

उदाहरण वाक्य

1. The Jacobson radical of a ring has various internal and external characterizations.
2. See the article " radical of a ring " for more of this.
3. The only idempotent contained in the Jacobson radical of a ring is 0.
4. In mathematics, specifically ring theory, the notion of "'quasiregularity "'provides a computationally convenient way to work with the Jacobson radical of a ring.
5. The concept of the Jacobson radical of a ring; that is, the intersection of all right / left simple right / left modules over a ring, is one example.
6. As a ring, it is sometimes a field, and often a direct product of fields; it can, though, contain non-zero nilpotents ( see radical of a ring ).
7. In yet a simpler way, we may think of the Jacobson radical of a ring as method to " mod out bad elements " of the ring  that is, members of the Jacobson radical act as 0 in the quotient ring, " R " / " J " ( " R " ).
8. The Jacobson radical of a ring consists of elements that satisfy a stronger property than being merely a non-unit  in some sense, a member of the Jacobson radical must not " act as a unit " in " any " canonical homomorphism to the zero of every " right division ring " ( each non-zero element of which has a right inverse ) internal to the ring in question.