We investigate the problem when tensor functor by a bimodule yields singular equivalence. It turns out that this is equivalent to one Hom given same induces triangle equivalence between homotopy categories of acyclic complexes injective modules. give conditions on appears in pair bimodules, defines with level. construct an explicit combinatorial manner, which quadratic monomial algebra and its ...

Let X be a codimension 1 subvariety of dimension > 1 of a variety of minimal degree Y . If X is subcanonical with Gorenstein canonical singularities admitting a crepant resolution, then X is Arithmetically Gorenstein and we characterise such subvarieties X of Y via apolarity as those whose apolar hypersurfaces are Fermat.

we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

Let (R, m, K) be a Gorenstein local ring of prime characteristic p > 0, and let x1, . . . , xn be a system of parameters. Let It = (x1, . . . , x t n)R for all t ≥ 1, and let u ∈ R represent a socle generator in R/I, where I = I1 = (x1, . . . , xn)R. Let y = x1 · · · xn. We have seen that E = lim −→ t R/It is an injective hull of K = R/m over R, where the map R/It → R/It+1 is induced by multipl...