An extension of differential Galois theory
H. F. Kreimer · Transactions of the American Mathematical Society · 1965
Introduction.The terminology and notation of this paper are taken from the author's paper The foundation for an extension of differential algebra [1].Let C be an associative, commutative coalgebra with identity over a ring W, which is freely generated as a W-module by a set M. If w -» w is a homomorphism of W into a ring S, let Cs be the S-module obtained from the W-module C by inverse transfer of the basic ring to S. If p is a homomorphism of a ring R into the algebra (Cs)* = Homs (CS,S), then for each me M there is a mapping a -» a"(m) of R into S, which will also be denoted by m, and the set of these mappings will be called an M-system of mappings of R into S. Let m -» Zn> p eM zm"p w ® p, where me M, zmnp e W> ana' zm<ip = 0 except for a finite number of elements n and /j in M, be the coproduct mapping of Cinto C (x)^ C;ifa, feeRandme AÍ, (a + b)m = am + bm and (ab)m= H",peMzmnP (an)(bp).An M-ring is a ring together with an M-