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mattbaker.blog | ||
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www.jeremykun.com
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| | | | | The First Isomorphism Theorem The meat of our last primer was a proof that quotient groups are well-defined. One important result that helps us compute groups is a very easy consequence of this well-definition. Recall that if $ G,H$ are groups and $ \varphi: G \to H$ is a group homomorphism, then the image of $ \varphi$ is a subgroup of $ H$. Also the kernel of $ \varphi$ is the normal subgroup of $ G$ consisting of the elements which are mapped to the identity under $ \varphi$. | |
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siddhartha-gadgil.github.io
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www.jeremykun.com
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| | | | | Last time we defined and gave some examples of rings. Recapping, a ring is a special kind of group with an additional multiplication operation that "plays nicely" with addition. The important thing to remember is that a ring is intended to remind us arithmetic with integers (though not too much: multiplication in a ring need not be commutative). We proved some basic properties, like zero being unique and negation being well-behaved. | |
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symomega.wordpress.com
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| | | I've just returned to Perth after giving one of the plenary talks at the "10th Slovenian Conference on Graph Theory" held in small ski-resort town of Kranjska Gora. I had never been to Slovenia before and hadn't realised how spectacularly beautiful it is. Lush green forests, steep mountains and azure alpine lakes complemented with a... | ||
