This note demonstrates that local rings of monoid algebras over regular rings are log-regular, indicating broader algebraic properties.
Local log-regular rings are Cohen–Macaulay local domains introduced by Kazuya Kato to expand the theory of toric varieties without a base. In this note, we show that local rings of monoid algebras over regular rings are log-regular. As a corollary, we show that monoid algebras are log-regular rings.
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Shinnosuke Ishiro (2026) studied this question.
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