Hello Could you please guys help me with the following exercise? Let a function defined by Show that es a homomorphism Is a rings isomorphism? Thanks
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Originally Posted by osodud Hello Could you please guys help me with the following exercise? Let a function defined by Show that is a homomorphism Is a rings isomorphism? Thanks What do the brackets represent in this case? The floor function? To show that its a homomorphism, show that and . Now try to see if and if is onto. If both are satisfied, its a ring isomorphism.
Originally Posted by osodud Hello Could you please guys help me with the following exercise? Let a function defined by Show that es a homomorphism Is a rings isomorphism? Thanks The homomorphism part follows from the fact that addition of congruence classes modulo is defined as (and the operation is well defined).
Originally Posted by Chris L T521 What do the brackets represent in this case? The floor function? The square brackets represent the equivalence class of the thing in the brackets - (equivalently, ). Essentially, (with ). Hint for part 2: Notice that ...So, how many elements are in , the image of the function ?
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