Algebra 2 by Ramji Lal

Author:Ramji Lal
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Exercises

7.1.1

Show that a noetherian domain is a U.F.D. if and only if g.c.d. exists in R.

7.1.2

Show that every proper ideal of a noetherian ring can be embedded in a maximal ideal.

7.1.3

Give an example of an integral domain in which every nonzero nonunit element is expressible as product of irreducible elements but still it is not a noetherian ring.

7.1.4

Is a direct product of noetherian rings a noetherian ring? Support.

7.1.5

Show that a vector space is noetherian if and only if it is finite dimensional.

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