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In this paper, we present a novel method for R-peak detection in the ElectroCardioGram (ECG) signal in a noisy environment. We interpret the R-peak occurrence as an irregularity in the signal. Thereby, we transform the problem of R-peaks detection into irregularity instants estimation. To point out these irregularities, we use an algebraic approach based on differential algebra and operational calculus. To make the R-peak detection more accuracy, we propose a new decision rule permitting a reliable distinction between R-peaks and false alarms. To assess the validity of theoretical analysis, numerical simulations, according to signals from the MIT-BIH arrhythmias database, are performed. To carry out the performance of the proposed method, a comparison with the most used technique in literature is achieved. The obtained results show the robustness of the algebraic method in the context of complicated pathologies as well as to various types of noises.