Structure of O(V) over full rings

On Projective Geometry over Full Matrix Rings

1. K. L. Chung, Fluctuation of sums of independent random variables, Ann. of Math. vol. 51 (1950) pp. 697-706. 2. K. L. Chung and P. Erdos, Probability limit theorems assuming only the first moment. I, Memoirs of the American Mathematical Society, no. 6, pp. 13-19. 3.-, On the lower limit of sums of independent random variables, Ann. of Math. vol. 48 (1947) pp. 1003-1013. 4. K. L. Chung and W. ...

Triangulaizability of Algebras Over Division Rings

Associated Graphs of Modules Over Commutative Rings

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

COTORSION DIMENSIONS OVER GROUP RINGS

Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.

Polynomial Rings over Pseudovaluation Rings

Let R be a ring. Let σ be an automorphism of R. We define a σ-divided ring and prove the following. (1) Let R be a commutative pseudovaluation ring such that x ∈ P for any P ∈ Spec(R[x,σ]) . Then R[x,σ] is also a pseudovaluation ring. (2) Let R be a σ-divided ring such that x ∈ P for any P ∈ Spec(R[x,σ]). Then R[x,σ] is also a σ-divided ring. Let now R be a commutative Noetherian Q-algebra (Q i...