Twenty years after the discovery of the F5 algorithm, Gr\"obner bases with signatures are still challenging to understand and to adapt to different settings. This contrasts with Buchberger's algorithm, which we can bend in many directions keeping correctness and termination obvious. I propose an axiomatic approach to Gr\"obner bases with signatures with the purpose of uncoupling the theory and the algorithms, and giving general results applicable in many different settings (e.g. Gr\"obner for submodules, F4-style reduction, noncommutative rings, non-Noetherian settings, etc.).

翻译：在发现F5算法20年后, Gr\“obner ” 带有签名的基数仍然难以理解和适应不同的设置。 这与Buchberger 的算法形成鲜明对比,我们可以在很多方向弯曲,保持正确性和终止性显而易见。 我提议对Gr\ “obner 基数采取不言自明的方法,签名的目的是将理论和算法脱钩,并给出适用于许多不同环境(例如, Gr\“obner ”, 用于子模量、 F4 式减缩、 非交替性环、 非诺黑环境等)的总体结果。