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For any non-torsion group $G$ with identity $e$ , we construct a strongly $G$ -graded ring $R$ such that the Jacobson radical $J (R_{e})$ is locally nilpotent, but $J (R)$ is not locally nilpotent. This answers a question posed by Puczyłowski.

On the object-wise tensor product of functors to modules.

Golasiński, Marek (2000)

Theory and Applications of Categories [electronic only]

On the structure of sequentially Cohen-Macaulay bigraded modules

Leila Parsaei Majd, Ahad Rahimi (2015)

Czechoslovak Mathematical Journal

Let $K$ be a field and $S = K [x_{1}, ..., x_{m}, y_{1}, ..., y_{n}]$ be the standard bigraded polynomial ring over $K$ . In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” $S$ -modules with respect to $Q = (y_{1}, ..., y_{n})$ . Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to $Q$ in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to $Q$ are considered.

Displaying 1 – 12 of 12

On Bernstein-Gelfand-Gelfand equivalence and tilting theory

On equivalence of graded rings.

On graded algebra bundles.

On induced modules over strongly group-graded algebras.

On regular semigroup rings.

On semigroup graded PI-algebras.

On the category of commutative connected graded Hopf algebras over a perfect field

On the Jacobson radical of graded rings.

On the Jacobson radical of graded rings

On the Jacobson radical of strongly group graded rings

On the object-wise tensor product of functors to modules.

On the structure of sequentially Cohen-Macaulay bigraded modules

Currently displaying 1 – 12 of 12