dedekind domain sentence - dedekind domain sentence in Hindi (1-10)

	1.	It is also universally catenary as it is a Dedekind domain.
	2.	Some authors add the requirement that a Dedekind domain not be a field.
	3.	In Dedekind domains, the situation is much simpler.
	4.	These are the prototypical examples of Dedekind domains.
	5.	This notion can be used to study the various characterizations of a Dedekind domain.
	6.	Now let M be a finitely generated module over an arbitrary Dedekind domain R.
	7.	For a Dedekind domain this is of course the same as the ideal class group.
	8.	Over an arbitrary Dedekind domain one has
	9.	In fact, every abelian group is isomorphic to the ideal class group of some Dedekind domain.
	10.	On the other hand, the ring of integers in a number field is always a Dedekind domain.

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