TES FORMAL MODUL PROJEKTIF DAN MODUL BEBAS ATAS RING OPERATOR DIFERENSIAL

Abstract

Suppose,,,,] 1 2 3 [n D  K d d d d d d linear differential operators with coefficients in K, which satisfy  a K; he = adi + ia. D is a linear differential carrier ring with the following properties: D not loading the divisor is zero, not commutative, and for every d d D i j, , i, j  1, , n and for every a, b  K apply i j i j i j ad (bd)  abd d  a ( b) d. Let M be a top module D formed from an ordinary differential linear system (OD) time-varying or partial differential linear (PD) system under control. Indicates M a projective module or a free module is used a formal test. The formal tests used are heavily dependent on characteristics of the module, ie For the projective module, the formal test used depends on kesurjektifan of the operator. As for the free module must be over a major ideal area.