Abstract
In this paper we study the problem of existence and uniqueness of solutions of implicit linear difference equations over commutative rings. The cases where the ring is integrally closed, Noetherian, local are considered. The question of periodic and quasi-polynomial solutions of this equation is also studied. In the case of a local ring, we obtain a formula for the solution of the equation as a series converging in $$\mathcal {M}$$ -adic topology, where $$\mathcal {M}$$ is the maximal ideal of the ring in question.
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