DBGRDakota Boys and Girls Ranch (North Dakota)
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Seen as an [A.sub.E]-ring, the DBGR [S.sup.*] [E; Z] (103) on a splitting domain ([z.sup.A], [c.sup.a]) is locally generated by the graded one-form d[z.sup.A], d[c.sup.i] such that
The DBGR [S.sup.*][E; Z] (103) is a minimal differential calculus over [A.sub.E]; that is, it is generated by elements df, f [member of] [A.sub.E].
Cohomology of the DBGR S* [E; Z] (103) is called the de Rham cohomology of an N-graded manifold (Z, AE).
The DBGR [S.sup.*.sub.[infinity]][F;Y] associated with an N-graded bundle (X, Y, [U.sub.F]) is defined as the direct limit