Let Λ be an Artinian algebra and F an additive subbifunctor of ExtΛ(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F -extensions have F -almost split sequences. Let T be an F -cotilting module in mod Λ and S a cotilting module over Γ = End(T ). Then Hom(−, T ) induces a duality between F -almost split sequences in ⊥F T and almost sp...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

The Gorenstein projective modules are proved to form a precovering class in the module category of a ring which has a dualizing complex. 0. Introduction This paper proves over a wide class of rings that the Gorenstein projective modules form a precovering class in the module category. Let me explain this statement. There are two terms of mystery, “Gorenstein projective modules” and “precovering...

Let (R, m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If GC -dimension of M/aM is finite for all ideals a generated by an R-regular sequence of length at most d − t then either GC -dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.

Harer has shown that the mapping class group is a virtual duality groupmirroring the work of Borel-Serre on arithmetic groups in semisimple Q-groups. Just as the homology of the rational Tits building provides the dualizing module for any torsion-free arithmetic group, the homology of the curve complex is the dualizingmodule for any torsion-free, finite index subgroup of the mapping class group...

Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...

an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

In the setting of geometric Langlands conjecture, we argue that phenomenon divergence at infinity on Bun_G (that is, difference between $!$-extensions and $*$-extensions) is controlled, Langlands-dually, by locus semisimple $\check{G}$-local systems. To see this, first rephrase question in terms Deligne-Lusztig duality then study functor DL_G^\spec acting spectral DG category IndCoh_N(LS_G). We...