On representation by continued fractions of elements of some special algebras

In this paper we consider continued fractions with elements from some special algebras. In absence of commutativity under multiplication, the study of properties of continued fractions is significantly complicated. For such fractions, some concepts related to classical continued fractions need to be modified. However, on the other hand, many properties of classical continued fractions are fulfilled for the generalized continued fractions under consideration. In particular, the values of the residuals are calculated using similar formulas. The most complete results can be obtained for continued fractions on the set of quaternions.