Ring Isomorphism to its Image (Abstract Algebra)

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[@anmolgrover8700]

Hey thank you very much for this! This is super helpful. Thank you!
Could you please, please make more videos on proving why certain functions from a ring to another ring is isomorphic with different examples and cases and add to your Abstract Algebra playlist? Students would really appreciate it!
Thank you! :)
Best regards

[@neharaj8737]

Sir i lIke your method of teaching great work😊
Sir i'm from india. One like from india👍

[@Dimiranger]

Nice video! Very informative :)

[@BriTheMathGuy]

Thanks very much! Glad to help.

[@katherinekelm7439]

Your function is not onto; there are many 2x2 matrices in M_2(R) that are not of the form (a b \\ -b a). If instead we defined phi from C to the set of all matrices of this form (which does form a ring), then phi would be a ring isomorphism.

[@BriTheMathGuy]

You are correct. This example is a ring isomorphism onto its image ,not all of M
_2 . Thanks for watching!