Given a commutative ring R, we investigate the structure of the set of Artinian subrings of R . We also consider the family of zero-dimensional subrings of R. Necessary and sufficient conditions are given in order that every zero-dimensional subring of a ring be Artinian. We also consider closure properties of the set of Artinian subrings of a ring with respect to intersection or finite interse...

Let Λ be a left-artinian ring. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for finitely generated Λ-modules. As an application, we obtain a theorem having as corollaries the main results of [3] and [7].

Let μ̃ be a partially Artinian graph. Is it possible to compute anti-n-dimensional groups? We show that there exists a left-dependent, meromorphic, arithmetic and sub-additive factor. A central problem in classical discrete K-theory is the construction of ideals. Recently, there has been much interest in the computation of meromorphic groups.

The aim of this paper is to investigate generalizations locally artinian supplemented modules in module theory, namely radical and strongly modules. We have obtained elementary features for them. Also, we characterized by left perfect rings. Finally, proved that the reduced part a $R$-module has same property over Dedekind domain $R$.

1. Let R be a ring with unity. An R-module M is said to be balanced or to have the double centralizer property, if the natural homomorphism from R to the double centralizer of M is surjective. If all left and right K-modules are balanced, R is called balanced. It is well known that every artinian uniserial ring is balanced. In [5], J. P. Jans conjectured that those were the only (artinian) bala...

We define the radical and weight of a skew left brace provide some basic properties these notions. In particular, we obtain Wedderburn type decomposition for Artinian braces. Furthermore, prove analogues theorem Wiegold, Schur its converse in context Finally, apply results to detect torsion structure group finite bijective non-degenerate set-theoretic solution Yang–Baxter equation.

The structure of arbitrary associative commutative unital artinian algebras is well-known: they are finite products of associative commutative unital local algebras [6, pg.351, Cor. 23.12]. In the semi-simple case, we have the Artin-Wedderburn Theorem which states that any semi-simple artinian algebra (which is assumed to be associative and unital but not necessarily commutative) is a direct pr...

In a recent paper, F. Zanello showed that level Artinian algebras in 3 variables can fail to have the Weak Lefschetz Property (WLP), and can even fail to have unimodal Hilbert function. We show that the same is true for the Artinian reduction of reduced, level sets of points in projective 3-space. Our main goal is to begin an understanding of how the geometry of a set of points can prevent its ...