Abstract Algebra | First Isomorphism Theorem for Rings

[@faraimudi7445]

Hi Mike! Which book/s would you recommend learning abstract algebra which transitions well from examples, theorems and definitions to proofs? Will religiously follow your videos, just found them helpful now. God bless you!

[@MichaelPennMath]

Judson is a nice open source option: abstract.ups.edu/ Gallian is a good choice too -- the newest edition is quite expensive, but you can probably find an older version. Dummit and Foote is more of a graduate text but is unmatched for the amount of examples and exercises.

[@hyperduality2838]

@@MichaelPennMath Same is dual to different. Isomorphism (absolute sameness) is dual to homomorphism (relative sameness, difference). Absolute truth is dual to relative truth -- Hume's fork. "Always two there are" -- Yoda.

[@maxryder9321]

1:51 does anyone have a link or a brief explanation of this shorter proof using abelian groups

[@antforeargar3523]

A ring is an abelian group where you can multiply too. Using the first isomorphism theorem for groups, the only thing left to check is that the function is also a homomorphism for multiplication, which is the only step that was left out (almost identical to the version for addition).

[@BaderMinawi]

Please Help me!!!!!

[@hyperduality2838]

Same is dual to different. Isomorphism (absolute sameness) is dual to homomorphism (relative sameness, difference). Absolute truth is dual to relative truth -- Hume's fork. "Always two there are" -- Yoda.