This paper introduces the Resilient Adaptive Algebraic Architecture, which is capable of adapting parallelism exploitation in a time-deterministic fashion to reduce power consumption, while meeting the existing real-time deadlines. Furthermore, the architecture provides low overhead error correction capabilities, through the use of algebraic properties of the operations it performs. We use two real-time industrial case studies to validate the architecture and to show how the adaptive exploitation works. Finally, we present the results of fault-injection campaigns to show the architecture resilience against soft-errors.