algebraic elementの例文
- Fields that do not allow any algebraic elements over them ( except their own elements ) are called algebraically closed.
- This characterization can be used to show that the sum, difference, product and quotient of algebraic elements over " K " are again algebraic over " K ".
- The minimal polynomial of an algebraic element " x " of " L " is irreducible, and is the unique monic irreducible polynomial of which " x " is a root.
- Algebraic number fields " K " come with a canonical norm function on them : the absolute value of the field norm " N " that takes an algebraic element " ? " to the product of all the rational integers, so it is a candidate to be a Euclidean norm on this ring.
- As a consequence, the depth of R in H is finite if and only if its " generalized quotient module " V represents an algebraic element in the representation ring ( or Green ring ) of R . This is the case for example if V is a projective module, or if V is a permutation module over a group algebra R ( i . e ., V has a basis that is a G-set ).
