division ring उदाहरण वाक्य

उदाहरण वाक्य

1. Division rings differ from fields only in that their multiplication is not required to be commutative.
2. The Artin Wedderburn theorem characterizes all simple Artinian rings as the matrix rings over a division ring.
3. However, by Wedderburn's little theorem all finite division rings are commutative and therefore finite fields.
4. Historically, division rings were sometimes referred to as fields, while fields were called  commutative fields.
5. Homogeneous coordinates for projective spaces can also be created with elements from a division ring ( skewfield ).
6. A commutative ring with unity satisfying the last condition is called a containment-division ring ( CDR ).
7. The Artin Zorn theorem generalizes the theorem to alternative rings : every finite alternative division ring is a field.
8. If " R " is a division ring or a field, then these are its only ideals.
9. The Artin Wedderburn theorem asserts that every semisimple ring is a finite product of full matrix rings over division rings.
10. The Weyl algebra is an example of a simple ring that is not a matrix ring over a division ring.