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Linear Differential Equation with Quasiperiodic Coefficient: A Question

I am reading the book Synergetics. The following passage is from the book: Assume that in the differential equation $\dot{q}= a(t)q$, where $a(t)$ is quasiperiodic, i. e., we assume that $a(t)$ ...
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Antiperiodic functions are indecomposable

Let $A$ be the algebra of continuous functions $\mathbb{R} \to \mathbb{R}$ which are periodic of period $1$, and write $M$ for the $A$-module of antiperiodic functions of period $1$ (meaning $f \in M$ ...