Abstract
For a polynomial ring, R,in 4 n variables over a field,we consider the submodule of R 4 corresponding to the 4 × 4n matrix made up of n groupings of the linear representation of quarternions with variable entries (which corresponds to the Cauchy-Fueter operator in partial differential equations) and let Mn be the corresponding quotient module. We compute many homological properties of Mn including the degrees of all of its syzygies,as well as its Betti numbers,Hilbert function,and dimension. We give similar results for its leading term module with respect to the degree reverse lexicographical ordering. The basic tool in the paper is the theory of
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
