i would really appreciate if you do it fast, i need urgently. i will give thumbs up. thankyou! Let R= Z, let M be the left R-module Z, and let X be(i)the subset, X = {12, 11, 9} C M .2.(a)Show that X generates M.(b)Is there any proper subset of X which also generates M?Either give an example (with justification), or explain why there is nosuch subset.

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Description: i would really appreciate if you do it fast, i need urgently. i will give thumbs up. thankyou! Let R= Z, let M be the left R-module Z, and let X be(i)the subset, X = {12, 11, 9} C M .2.(a)Show that X generates M.(b)Is there any proper subset of X whi

It is given that, R = ℤ and M be the left R-module of ℤ and X = 12, 11, 9⊂M be any subset of M.…

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2. (i) Let R = Z, let M be the left R-module Z, and let X be the subset, X = {12, 11,9} CM. Show that X generates M. (a) (b) Is there any proper subset of X which also generates M? Either give an example (with justification), or explain why there is no such subset.

2. (i) Let R = Z, let M be the left R-module Z, and let X be the subset, X = {12, 11,9} CM. Show that X generates M. (a) (b) Is there any proper subset of X which also generates M? Either give an example (with justification), or explain why there is no such subset.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 32E: 32. a. Let be an ideal of the commutative ring and . Prove that the setis an ideal of containing...

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