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A ring R is said to have property (◇) if the injective hull of every simple R-module is locally Artinian. By landmark results of Matlis and Vamos, every commutative Noetherian ring has (◇). We give a systematic study of commutative rings with (◇), We give several general characterizations in...
Let A be a representation-finite self-injective algebra over an algebraically closed field k. We give a new characterization for an orthogonal system in the stable module category...
We study the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. We show that a tame algebra in this class is simply connected if and only if its...
Let A and B be two Morita equivalent finite dimensional associative algebras over a field 𝕜. It is well known that Hochschild cohomology is invariant under Morita equivalence. Since infinitesimal deformations are connected with the second Hochschild cohomology group, we explicitly describe the...
We study syzygies of (maximal) Cohen–Macaulay modules over one dimensional Cohen–Macaulay local rings. We assume that rings are generically Gorenstein. We compare these modules to Cohen–Macaulay modules over the endomorphism ring of the maximal ideal. After this comparison, we give several...
We study the universal enveloping associative conformal algebra for the central extension of a current Lie conformal algebra at the locality level N = 3. A standard basis of defining relations for this algebra is explicitly calculated. As a corollary, we find a linear basis of the free...
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