integral basis in Hindi - integral basis meaning in Hindi

	1.	A classical result, based on a result of David Hilbert, is that a tamely ramified abelian number field has a normal integral basis.
	2.	In cases where the theorem states that a normal integral basis does exist, such a basis may be constructed by means of Gaussian periods.
	3.	For example if we take a prime number, has a normal integral basis consisting of all the-th roots of unity other than.
	4.	It is an integer, and is an invariant property of the field " F ", not depending on the choice of integral basis.
	5.	:Each finite tamely ramified abelian extension of a fixed number field has a relative normal integral basis if and only if "'Q "'} }.
	6.	If is a square-free integer and ) } } is the corresponding quadratic field, then is a ring of quadratic integers and its integral basis is given by ) / 2 ) } } if and by ) } } if.
	7.	In the other direction, given a pair ( X, \ omega ) where X is a compact Riemann surface and \ omega a holomorphic 1-form one can construct a polygon by using the complex numbers \ int _ { \ gamma _ j } \ omega where \ gamma _ j are disjoint paths between the zeroes of \ omega which form an integral basis for the relative cohomology.

integral basis meaning in Hindi