Beckner, William2010-12-012010-12-012017-05-112010-12-012010-12-012017-05-112010-05May 2010http://hdl.handle.net/2152/ETD-UT-2010-05-1504textThis paper covers basic theory of Grobner Bases and an algebraic analysis of the linear constant coefficient partial differential operators, specifically the Cauchy-Fueter operator. We will review examples and theory of regular and biregular functions in several quaternionic variables.application/pdfengGröbner basisCauchy-FueterBiregularQuaternionicGröbner basis theory and its applications for regular and biregular functionsthesis2010-12-01