However, if is an infinite field, any partial spread with fewer than } } members can be extended and the translation net can be completed to an affine translation plane.
12.
Over an infinite field, the twisted polynomial ring is isomorphic to the ring of additive polynomials, but where multiplication on the latter is given by composition rather than usual multiplication.
13.
If, however, we choose a nice infinite field then we can conclude that two polynomials are equal iff their evaluation maps are equal, and these " can " be composed.
14.
But the " reverse of truth " _ the invented tale, the alibi, the distortion and the concealment _ " has a hundred thousand faces and an infinite field ."
15.
It is equivalent to assume that this equality holds for all " a " and " b " in some infinite field containing " k ", such as its algebraic closure.
16.
Hochster ); for example, if the ring " R " contains an infinite field or a finite field of sufficiently large cardinality, then the statement follows from a fact in linear algebra that a vector space over an infinite field or a finite field of large cardinality is not a finite union of its proper vector subspaces.
17.
Hochster ); for example, if the ring " R " contains an infinite field or a finite field of sufficiently large cardinality, then the statement follows from a fact in linear algebra that a vector space over an infinite field or a finite field of large cardinality is not a finite union of its proper vector subspaces.
18.
Physically, this represents a uniform plane wave propagating in the plane of the FSS . In the spatial domain, the coherent summation of all of the spatial domain Green's function's becomes infinite, so that any finite current produces an infinite field on the surface of the FSS . As a result, all currents must be zero under this condition.
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