Pith. Sign in

RECORD

b-generalized skew derivations acting as 2-Jordan multiplier on multilinear polynomials in prime rings

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Mani Shankar Pandey, Ashutosh Pandey

Group Theory · Submitted 6 Dec 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Consequently, we discuss the cases when this identity acts as Jordan derivation and 2- Jordan multiplier on prime rings

how it is stated · asserted 0.88 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2212.02892 (version 2)
Pith IDSSTEXSAK, Pith's permanent record of this paper and its review
CitationAshutosh Pandey, Mani Shankar Pandey. "b-generalized skew derivations acting as 2-Jordan multiplier on multilinear polynomials in prime rings." arXiv:2212.02892 (2022). https://pith.science/paper/SSTEXSAK
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,786 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Let R be a prime ring of characteristic not equal to 2, U be its Utumi quotient ring and C be the extended centroid of R. Let \phi be a multilinear polynomial over C, which is not central valued on R and F, G be two b-generalized skew derivations on R. The purpose of this article is to describe all possible forms of the b-generalized skew derivations F and G satisfying the identity $F (u)u + uG(u) = G(u ^2)$, for all u \in {{\phi}({\zeta}) | {\zeta} = ({\zeta}1 . . . , {\zeta}n) \inR^n}. Consequently, we discuss the cases when this identity acts as Jordan derivation and 2- Jordan multiplier on prime rings

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let R be a prime ring of characteristic not equal to 2, U be its Utumi quotient ring and C be the extended centroid of R. background 1.00 0.07 0.02 asserted 0.95
s1 Let \phi be a multilinear polynomial over C, which is not central valued on R and F, G be two b-generalized skew derivations on R. background 1.00 0.10 0.02 asserted 0.85
s2 The purpose of this article is to describe all possible forms of the b-generalized skew derivations F and G satisfying the identity $F (u)u + uG(u) = G(u ^2)$, for all u \in {{\phi}({\zeta}) | {\zeta} = ({\zeta}1 . . . , {\zeta}n) \inR^n}. contribution 0.98 0.63 0.18 asserted 0.91
s3 Consequently, we discuss the cases when this identity acts as Jordan derivation and 2- Jordan multiplier on prime rings contribution 0.66 0.84 0.21 asserted 0.88

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Let R be a prime ring of characteristic not equal to 2, U be its Utumi quotient ring and C be the extended centroid of R. Let \phi be a multilinear polynomial over C, which is not central valued on R and F, G be two b-generalized skew derivations on R. The purpose of this article is to describe all possible forms of the b-generalized skew derivations F and G satisfying the identity $F (u)u + uG(u) = G(u ^2)$, for all u \in {{\phi}({\zeta}) | {\zeta} = ({\zeta}1 . . . , {\zeta}n) \inR^n}. Consequently, we discuss the cases when this identity acts as Jordan derivation and 2- Jordan multiplier on prime rings

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.