In this paper we generalize a result of Urban on the structure of residually reducible representations on local Artinian rings from the case that the semi-simplification of the residual representation splits into 2 absolutely irreducible representations to the case where it splits into m ≥ 2 absolutely irreducible representations.

Under the assumption that a residually finite-dimensional Hopf algebra H has an Artinian ring of fractions, it is proved flat module over any right coideal subalgebra satisfying polynomial identity and faithfully subalgebra. As consequence we find large class algebras which are all subalgebras subalgebras.

There has been much work on strong and weak Lefschetz conditions for graded Artinian algebras A, especially those that are Gorenstein. A more general invariant of an algebra or finite A-module M we consider here is the set Jordan types elements maximal ideal

The aim of this paper is to investigate strong notion strongly ⨁-supplemented modules in module theory, namely ⨁-locally artinian supplemented modules. We call a M if it locally and its supplement submodules are direct summand. In study, we provide the basic properties particular, show that every summand supplemented. Moreover, prove ring R semiperfect with radical only projective R-module

Let Λ be an Auslander’s 1-Gorenstein Artinian algebra with global dimension two. If Λ admits a trivial maximal 1-orthogonal subcategory of modΛ, then for any indecomposable module M ∈ modΛ, we have that the projective dimension of M is equal to one if and only if so is its injective dimension and that M is injective if the projective dimension of M is equal to two. In this case, we further get ...

We extend the “linearly exponential” bound for the Castelnuovo-Mumford regularity of a graded ideal in a polynomial ring K[x1, . . . , xr] over a field (established by Galligo and Giusti in characteristic 0 and recently, by Caviglia-Sbarra for abitrary K) to graded submodules of a graded module over a homogeneous Cohen-Macaulay ring R = ⊕n≥0Rn with artinian local base ring R0. As an application...

Suppose we are given a set M . E. Kolmogorov’s derivation of functions was a milestone in statistical measure theory. We show that Ψ̃ is homeomorphic to Rκ,K . The work in [5] did not consider the ultra-one-to-one, finitely Maclaurin, p-adic case. It is essential to consider that ι may be semi-simply Artinian.

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-...

Ladders were introduced by Igusa and Todorov for the investigation of representation-finite artinian algebras and algebras over an algebraically closed field [7]. They prove a radical layers theorem [7] which exhibits the graded structure of Auslander-Reiten sequences. In a second article [8] they obtain a characterization of the Auslander-Reiten quivers of representation-finite artinian algebr...

Let R = ⊕ n≥0 Rn be a homogeneous Noetherian ring with local base ring (R0,m0) and let M be a finitely generated graded R-module. Let Hi R+ (M) be the i-th local cohomology module of M with respect to R+ := ⊕ n>0 Rn. If dimR0 ≤ 1, the R-modules Γm0R(H R+ (M)), (0 :Hi R+ (M) m0) and Hi R+ (M)/m0H i R+ (M) are Artinian for all i ∈ N0. As a consequence, much can be said on the asymptotic behaviour...