Skip to content
DraconiticResearch
Search Sources API
181,716 studies31 sourcesUpdated 18 min ago
PreprintCC BY 4.0arXiv

A Reduced Non-McCoy Ring with the Annihilator Condition and (A2)

  • Viet-Hoang Tran
  • Tan M. Nguyen
Open at sourcePDFDOICite

Abstract

It has been asked whether a reduced non-McCoy ring can satisfy both the annihilator condition and (An) for some n ≥ 2. In this work, we prove that such rings exist exactly when n=2, by constructing a countable example and showing that the annihilator condition together with (A3) forces a ring to be McCoy.

Related

  1. Annihilator Multiplication Modules: Ring Characterizations and Constructions
    Hwankoo Kim, Suat Koç
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. Reduced APN permutations and a disproof of the Galois-ring lifting conjecture
    Daniele Bartoli, Pantelimon Stanica
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Deterministic Determination of Axial Constants, Sectional Regularities and Annihilator Numbers
    Amir Hashemi, Rozhin Sadr, Werner M. Seiler
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Self-Orthogonal τ-Tilting Modules and Tilting Modules II: Annihilator Separation
    Xiaojin Zhang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Classification of three-dimensional Leibniz dialgebras with two-dimensional annihilator
    Naurizbay Uzakbaev
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{tran2026reduced,
  title = {{A Reduced Non-McCoy Ring with the Annihilator Condition and $(A_2)$}},
  author = {Viet-Hoang Tran and Tan M. Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00116},
  eprint = {2610.00116},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00116},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Reduced Non-McCoy Ring with the Annihilator Condition and (A_2)
AU  - Viet-Hoang Tran
AU  - Tan M. Nguyen
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00116
UR  - https://arxiv.org/abs/2610.00116
AB  - It has been asked whether a reduced non-McCoy ring can satisfy both the annihilator condition and (A_n) for some n ≥ 2. In this work, we prove that such rings exist exactly when n=2, by constructing a countable example and showing that the annihilator condition together with (A_3) forces a ring to be McCoy.
ER  -