Radicals of Polynomial Rings in Non-commutative Indeterminates.
We study finitely generated bigraded Buchsbaum modules over a standard bigraded polynomial ring with respect to one of the irrelevant bigraded ideals. The regularity and the Hilbert function of graded components of local cohomology at the finiteness dimension level are considered.
We introduce the notion of a relative hermitian Morita context between torsion triples and we show how these induce equivalences between suitable quotient categories of left and right modules.Due to the lack of involutive bimodules, the induced Morita equivalences are not necessarily hermitian, however.
We generalize the notion of a coarse sequential convergence compatible with an algebraic structure to a coarse one in a given class of convergences. In particular, we investigate coarseness in the class of all compatible convergences (with unique limits) the restriction of which to a given subset is fixed. We characterize such convergences and study relative coarseness in connection with extensions and completions of groups and rings. E.g., we show that: (i) each relatively coarse dense group precompletion...