Extension of An Ideal
Let A and B be two commutative rings with unity, and let f : A → B be a (unital) ring homomorphism. If is an ideal in A, then need not be an ideal in B (e.g. take f to be the inclusion of the ring of integers Z into the field of rationals Q). The extension of in B is defined to be the ideal in B generated by . Explicitly,
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Famous quotes containing the words extension of, extension and/or ideal:
“The medium is the message. This is merely to say that the personal and social consequences of any medium—that is, of any extension of ourselves—result from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.”
—Marshall McLuhan (1911–1980)
“The medium is the message. This is merely to say that the personal and social consequences of any medium—that is, of any extension of ourselves—result from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.”
—Marshall McLuhan (1911–1980)
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