This article explores equalizing properties in semirings, indicating their applications in distributive lattices.
The article studies multiplicatively idempotent semirings with additional conditions (annihilator condition, equalizing properties). For such semirings, the equalizing properties are studied (Theorems 1–3, Proposition 1). The results obtained can be applied to distributive lattices (Propositions 2–4). The work provides examples and explanatory notes.
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E. M. Vechtomov (2025) studied this question.
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