Flat modules and Gröbner bases over truncated discrete valuation rings

MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」We present basic properties of Groebner bases of submodules of a free module of finite rank over a polynomial ring with coefficients in a tdvr (:= truncated discrete valuations ring). As an application, we give a criterion for an algebra of finite type over a tdvr to be flat and prove the existence of a flat lifting of a flat algebra over a tdvr