On Derivationally Prime Rings

Abstract

The Parisi-Sourlas mechanism is demonstrated directly for fields over pseudo-Euclidean space, without the use of Wick rotations, superspace or Berezin integration. An irreducible field supermultiplet for the Lie superalgebra iosp( m, 4 2 ) is constructed using a modified version of the method of produced representations, and a (1, 1)-dimensional reduction obtained through examination of the metric.

Jacobson Radicals of Ore Extensions of Derivation Type

“…Basic properties of R X D can be found in Burkov (1980). Polynomials in R X D can be written in the form a 0 t 0 + a 1 t 1 + · · · + a n t n where a 0 a n ∈ R and where t 0 t n are distinct words in indeterminates x i .…”

Quotient Rings of Ore Extensions with More than One Indeterminate

“…Basic properties of R X D can be found in Burkov (1980). If X consists of a single element x, we denote R X D by R x , where = x .…”

Symmetric Utumi quotient rings of Ore extensions by skew derivations

“…Given a map φ : X → L, let R[X; φ] denote the ring of polynomials in noncommuting indeterminates x ∈ X and with coefficients in R subjected to the following commutation rule for a ∈ R and x ∈ X: xa = σ(a)x + δ(a), where δ = φ(x) is a σ-derivation. [4,6,25,26].) We stress here that the indeterminates x ∈ X do not commute with each other.…”

“…This topic has been extensively studied in various directions for a few decades. See, for example, [4,5,6,7,10,11,12,13,16,17,25,26].…”