Properties of The Trace
As mentioned above, the trace TrL/K : L → K is a K-linear map. Additionally, it behaves well in towers of fields: if M is a finite extension of L, then the trace from M to K is just the composition of the trace from M to L with the trace from L to K, i.e.
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—Ralph Waldo Emerson (1803–1882)
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—John Locke (1632–1704)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
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—Ralph Waldo Emerson (1803–1882)