we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

The so-called ’change-of-ring’ results are well-known expressions which present several connections between projective, injective and flat dimensions over the various base rings. In this note we extend these results to the Gorenstein dimensions over Cohen-Macaulay local rings.

Abstract We introduce the cohomological blowup of a graded Artinian Gorenstein algebra along surjective map, which we term BUG (blowup Gorenstein) for short. This is intended to translate an algebraic context cohomology ring projective manifold submanifold. show, among other things, that connected sum, it general fiber in flat family algebras, and preserves strong Lefschetz property. also show ...

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated le...

We proved in Theorem 3. 15 b that free modules have the precise same property that. projective modules 2 attributes to projective modules. In fact, it is easy to use.BIG PROJECTIVE MODULES ARE FREE. Finitely generated proiective modules rise significantly in certain geometric nd.dorff space X and finitely generated projective modules over the ring of continuous real-valued functions on X. A num...

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions rarely come with practical and robust criteria for finiteness, even over commutative noetherian local rings. Indeed, over such a ring ...

We study Enriques surfaces with four disjoint A2-configurations. In particular, we construct open Enriques surfaces with fundamental groups (Z/3Z) × Z/2Z and Z/6Z, completing the picture of the A2-case from [10]. We also construct an explicit Gorenstein Q-homology projective plane of singularity type A3 + 3A2, supporting an open case from [7].