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I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ...
I need help with yet another aspect of Example 1.14 ... ...
Example 1.14 reads as follows:
Near the end of the above text from T. Y. Lam we read the following:
" ... ... Moreover ##R \oplus M## and ##M \oplus S## are both ideals of ##A##, with ##A / (R \oplus M ) \cong S## and ##A / ( M \oplus S ) \cong R## ... ... "Can someone please help me to show, formally and rigorously that ##A / (R \oplus M ) \cong S## and ##A / ( M \oplus S ) \cong R## ... ...My only thought so far is that the First Isomorphism Theorem for Rings may be useful ...
Hope someone can help ... ...
Peter
I need help with yet another aspect of Example 1.14 ... ...
Example 1.14 reads as follows:
" ... ... Moreover ##R \oplus M## and ##M \oplus S## are both ideals of ##A##, with ##A / (R \oplus M ) \cong S## and ##A / ( M \oplus S ) \cong R## ... ... "Can someone please help me to show, formally and rigorously that ##A / (R \oplus M ) \cong S## and ##A / ( M \oplus S ) \cong R## ... ...My only thought so far is that the First Isomorphism Theorem for Rings may be useful ...
Hope someone can help ... ...
Peter
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