Book Review: Polynomial identity rings

Differential Polynomial Rings of Triangular Matrix Rings

Identity page of Social Science Quarterly Book Review

Efficient Identity Testing and Polynomial Factorization in Nonassociative Free Rings

In this paper we study arithmetic computations over non-associative, and non-commutative free polynomials ring F{x1, x2, . . . , xn}. Prior to this work, the non-associative arithmetic model of computation was considered by Hrubes, Wigderson, and Yehudayoff [HWY10]. They were interested in completeness and explicit lower bound results. We focus on two main problems in algebraic complexity theor...

On strongly J-clean rings associated with polynomial identity g(x) = 0

In this paper, we introduce the new notion of strongly J-clean rings associated with polynomial identity g(x) = 0, as a generalization of strongly J-clean rings. We denote strongly J-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-J-clean rings. Next, we investigate some properties of strongly g(x)-J-clean.

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...