integral domain meaning in Hindi

Examples

1. A regular ring is reduced but need not be an integral domain.
2. The proof uses induction so it does not apply to all integral domains.
3. Notice also that the unit in that integral domain.
4. A B�zout domain is an integral domain in which B�zout's identity holds.
5. This shows that integral domains and division rings don't have such idempotents.
6. Rational expressions are the quotient field of the polynomials ( over some integral domain ).
7. If however R is not an integral domain, then the conclusion need not hold.
8. First adjoin negatives to get an integral domain, then take its field of fractions.
9. "Integral domain " is defined almost universally as above, but there is some variation.
10. Noncommutative integral domains are sometimes admitted.