Radical Ideals and their Varieties - University of Utah
Radical Ideals and their Varieties
The Strong Nullstellensatz
Priyank Kalla
Associate Professor Electrical and Computer Engineering, University of Utah
kalla@ece.utah.edu kalla
Nov 6, 2017 - onwards
Agenda
Study (strong/exact) relationships between ideals and varieties Based on the Regular and Strong Nullstellensatz result
These results are needed for word-level verification of circuits The remaining concepts that enable complete hardware verification:
Study Nullstellensatz over algebraically closed fields Then study Nullstellensatz over Galois fields F2k and hardware design (I'll give you my textbook chapters) Then apply Nullstellensatz specifically over F2k to verify digital circuits We should be able to study these basic concepts in the next 3-4 lectures and then apply these concepts to practical datapath circuits.
P. Kalla (Univ. of Utah)
Radicals and I (V (J))
Nov 6, 2017 - onwards 2 / 22
Before we get to Strong Nullstellensatz...
Some more concepts about Varieties Let F be a field and a F be an arbitrary point
P. Kalla (Univ. of Utah)
Radicals and I (V (J))
Nov 6, 2017 - onwards 3 / 22
Before we get to Strong Nullstellensatz...
Some more concepts about Varieties Let F be a field and a F be an arbitrary point a is a variety of some ideal: find J s.t. V (J) = {a}
P. Kalla (Univ. of Utah)
Radicals and I (V (J))
Nov 6, 2017 - onwards 3 / 22
Before we get to Strong Nullstellensatz...
Some more concepts about Varieties Let F be a field and a F be an arbitrary point a is a variety of some ideal: find J s.t. V (J) = {a} J = x-a
P. Kalla (Univ. of Utah)
Radicals and I (V (J))
Nov 6, 2017 - onwards 3 / 22
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