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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“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“‘Tis chastity, my brother, chastity.
She that has that is clad in complete steel,
And like a quivered nymph with arrows keen
May trace huge forests and unharbored heaths,
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Where, through the sacred rays of chastity,
No savage fierce, bandit, or mountaineer
Will dare to soil her virgin purity.”
—John Milton (1608–1674)