quotient ring उदाहरण वाक्य

उदाहरण वाक्य

1. The quotient ring of a Boolean ring modulo a ring ideal corresponds to the factor algebra of the corresponding Boolean algebra modulo the corresponding order ideal.
2. An easy motivational example is the quotient ring \ mathbb { Z } / n \ mathbb { Z } for any integer n > 1.
3. For other examples of quotient objects, see quotient ring, quotient space ( linear algebra ), quotient space ( topology ), and quotient set.
4. By extension, in abstract algebra, the term quotient space may be used for quotient modules, quotient rings, quotient groups, or any quotient algebra.
5. The naive solution is to replace the fraction field by the total quotient ring, that is, to invert every element that is not a zero divisor.
6. Hence we may localize the ring R at the set S to obtain the total quotient ring S ^ {-1 } R = Q ( R ).
7. If R is a domain, then S = R-\ { 0 \ } and the total quotient ring is the same as the field of fractions.
8. Any nonzero element of the quotient ring will differ by a null sequence from such a sequence, and by taking pointwise inversion we can find a representative inverse element.
9. From the point of view of abstract algebra, congruence modulo n is a congruence relation on the ring of integers, and arithmetic modulo n occurs on the corresponding quotient ring.
10. The total quotient ring Q ( A \ times B ) of a product ring is the product of total quotient rings Q ( A ) \ times Q ( B ).