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Semigroup rings over semiprime ring semigroups
2019We consider semigroup rings over a particular class of semigroups: those semigroups which arise as the multiplicative semigroup of a ring.
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Ruthenium-Catalyzed Cycloadditions to Form Five-, Six-, and Seven-Membered Rings
Chemical Reviews, 2021Rosalie S Doerksen +2 more
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Semiprime rings with differential identities
1992Let \(R\) be a semi-prime ring with maximal right quotient ring \(U\) and let \(\text{Der}(U)\) be the set of derivations of \(U\). The extended centroid of \(R\) is \(C\), the center of \(U\). A differential polynomial is an element \(f \in U*_ C C\{X^ W\}\), the free product over \(C\) of \(U\) and the free \(C\)-algebra in indeterminates \(x_ i^ w\),
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On semiprime Noetherian PI-rings
2016Let \(R\) be a semiprime Noetherian PI-ring, and let \(Q\) be its semisimple Artinian classical quotient ring. The author establishes the equivalence of the following three statements. (1) The (classical) Krull dimension of \(R\) is \(\leq 1\); (2) If \(T\) is a ring with \(R\subseteq T\subseteq Q\), then \(T\) is Noetherian; (3) For central regular ...
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Cleavage of Carbon–Carbon σ-Bonds of Four-Membered Rings
Chemical Reviews, 2021Masahiro Murakami, Naoki Ishida
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Stereoselective construction of β-, γ- and δ-lactam rings via enzymatic C–H amidation
Nature Catalysis, 2023David A Vargas +2 more
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Construction of Medium-Sized Rings by Gold Catalysis
Chemical Reviews, 2021Ronald L Reyes +2 more
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