We investigate {left, right, middle} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov's notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov's Problem # 18 and its generalizations are obtained. Several related problems remain open.
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Mathematics
, 2025, Issue 1, pp. 1–10
ISSN Online: 0000-0000
DOI:
10.xxxx/example-doi