The nature of the divisors of a Noetherian ring A provides a window to examine its arithmetical and geometric properties. Here we examine the divisors of Rees algebras of ideals{the so called blowup algebras{from the perspective of the operation of shifting. It permits the organization of some previous results in a more structured manner and at the same time predicts the occurrence of several n...

let r be a right gf-closed ring with finite left and right gorenstein global dimension. we prove that if i is an ideal of r such that r/i is a semi-simple ring, then the gorensntein flat dimensnion of r/i as a right r-module and the gorensntein injective dimensnnion of r/i as a left r-module are identical. in particular, we show that for a simple module s over a commutative gorensntein ring r, ...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

We define generalized Koszul modules and rings develop a theory for N-graded with the degree zero part noetherian semiperfect. This specializes to classical graded artinian semisimple developed by Beilinson-Ginzburg-Soergel ungraded semiperfect Green Martinéz-Villa. Let A be left finite ring generated in 1 A0 semiperfect, J its Jacobson radical. By dual of we mean Yoneda Ext Ext_A•(A/J,A/J). If...

we consider the class $mathfrak m$ of $bf r$--modules where $bf r$ is an associative ring. let $a$ be a module over a group ring $bf r$$g$, $g$ be a group and let $mathfrak l(g)$ be the set of all proper subgroups of $g$. we suppose that if $h in mathfrak l(g)$ then $a/c_{a}(h)$ belongs to $mathfrak m$. we investigate an $bf r$$g$--module $a$ such that $g not = g'$, $c_{g}(a) = 1$. we stud...

In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient) morphisms. Then give a characterization new concept. We show that an epimorphism p:Y→U is if and only for any right R-module Z morphism g:Z→Y such pg finitely-copartial isomorphism (singly-copartial isomorphism) from to Y with codomain U finitely (singly) split epimorphism. also investigate relation...

‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...

A right Johns ring is a Noetherian in which every ideal annihilator. It known that RR the Jacobson radical J(R)J(R) of nilpotent and Soc(R)(R) an essential RR. Moreover, Kasch, is, simple RR-module can be embedded For M∈RM∈R-Mod we use concept MM-annihilator define module (resp. quasi-Johns) as MM such submodule MM-annihilator. called quasi-Johns if any set submodules satisfies ascending chain ...

For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...