Abstract In this paper, we study the strong nil-cleanness of certain classes of semigroup rings. For a completely 0-simple semigroup M = ℳ 0 ( G ; I , Λ ; P ) M={ {\mathcal M} }^{0}(G;I,\text{Λ};P) , we show that the contracted semigroup ring R 0 [ M ] {R}_{0}{[}M] is strongly nil-clean if and only if either | I | = 1 |I|=1 or | Λ | = 1 |\text{Λ}|=1 , and R [ G ] R{[}G] is strongly nil-clean; as a corollary, we characterize the strong nil-cleanness of locally inverse semigroup rings. Moreover, let S = [ Y ; S α , φ α , β ] S={[}Y;{S}_{\alpha },{\varphi }_{\alpha ,\beta }] be a strong semilattice of semigroups, then we prove that R [ S ] R{[}S] is strongly nil-clean if and only if R [ S α ] R{[}{S}_{\alpha }] is strongly nil-clean for each α ∈ Y \alpha \in Y .

中文翻译：

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半群环的强零净性

摘要 本文研究了某些类半群环的强零净性。对于完全 0-简单半群 M = ℳ 0 ( G ; I , Λ ; P ) M={ {\mathcal M} }^{0}(G;I,\text{Λ};P) ，我们证明收缩半群环 R 0 [ M ] {R}_{0}{[}M] 是强零净当且仅当 我| = 1 |I|=1 或 | Λ | = 1 |\text{Λ}|=1 ，并且 R [ G ] R{[}G] 是非常零干净的；作为推论，我们表征了局部逆半群环的强零清洁性。此外，令 S = [ Y ; S α , φ α , β ] S={[}Y;{S}_{\alpha },{\varphi }_{\alpha ,\beta }] 是半群的强半格，那么我们证明 R [ S ] R{[}S] 是强零净当且仅当 R [ S α ] R{[}{S}_{\alpha }] 对于每个 α ∈ Y \alpha \in Y 是强零净.