We present a new algorithm to determine retracts in algebras, revealing correct definitions for Yang-Baxter solutions.
We present a general description of the notion of a retract of an algebra with a set of binary operations and describe an algorithm for finding the retract. We apply the result to fill a gap and give a correct definition of multipermutation degenerate set-theoretical solutions of the Yang–Baxter equation which has not been established so far.
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Jedlička et al. (2026) studied this question.
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