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<p>Strongly nil-cleanness is an important property in the theory of rings. The aim of this note is to probe the strongly nil-cleanness of semigroup rings. The new conditions for a semigroup ring to be strongly nil-clean are obtained. These refine the first two authors’ related results (<i>J. Algebra Appl.</i> 24(2025) 2550245 doi: 10.1142/S0219498825502457). Also, we give new criterions for a semigroup ring to be uniquely nil-clean.</p>

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Strongly nil-clean semigroup rings revisited

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • Junying Guo,
  • Xiaojiang Guo,
  • Kai Zhu

摘要

Strongly nil-cleanness is an important property in the theory of rings. The aim of this note is to probe the strongly nil-cleanness of semigroup rings. The new conditions for a semigroup ring to be strongly nil-clean are obtained. These refine the first two authors’ related results (J. Algebra Appl. 24(2025) 2550245 doi: 10.1142/S0219498825502457). Also, we give new criterions for a semigroup ring to be uniquely nil-clean.