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Analysis on generalized superspaces. (English) Zbl 0612.58009
In the past few years there have been made several attempts to generalize the so-called super-mathematics to cases where the domain of scalars is not just a Grassmann algebra but any associative $$\sigma$$-commutative G- graded algebra A (G is an abelian group, $$\sigma$$ a commutation factor on G). In addition to the references cited by the authors one might also mention the work by R. Trostel [Hadronic J. 6, 1518-1578 (1983; Zbl 0559.58003), and ibid., 305-405 (1983; Zbl 0533.58012)].
The present work, too, deals with this problem. Starting from their preparatory work [J. Math. Phys. 25, 3367-3374 (1984; Zbl 0558.17006)] the authors first specify their algebra of ”supernumbers” A and define the corresponding ”superspaces”, some of the basic concepts and theorems of classical analysis like differentiation, Taylor expansion, the inverse mapping theorem, and integration.
Reviewer: M.Scheunert

##### MSC:
 58C50 Analysis on supermanifolds or graded manifolds 58A50 Supermanifolds and graded manifolds 15A78 Other algebras built from modules 16W50 Graded rings and modules (associative rings and algebras)