Abstract
Formal series over a group are studied as an algebraic system with componentwise composition and a partial operation of convolution “”. For right-ordered groups a module of formal power series is introduced and studied; these are formal sums with well-ordered supports. Special attention is paid to systems of formal power series (whose supports are well-ordered with respect to the ascending order) that form an -basis, that is, such that every formal power series can be expanded uniquely in this system. -bases are related to automorphisms of the module of formal series that have natural properties of monotonicity and -linearity. The relations and are also studied. Note that in the case of a totally ordered group the system of formal power series forms a skew field with valuation (Mal'tsev-Neumann, 1948-1949.).
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