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Abstract <p>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.</p>

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On Multiplicatively Idempotent Semirings with Additional Conditions

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • E. M. Vechtomov

摘要

Abstract

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.