On zero-symmetric nearrings with identity whose additive groups are simple

Wen-Fong Ke; Johannes H. Meyer; Günter F. Pilz; Gerhard Wendt

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 869-880
  • ISSN: 0011-4642

Abstract

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We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group Sym ( ℕ ) as its additive group.

How to cite

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Ke, Wen-Fong, et al. "On zero-symmetric nearrings with identity whose additive groups are simple." Czechoslovak Mathematical Journal 74.3 (2024): 869-880. <http://eudml.org/doc/299296>.

@article{Ke2024,
abstract = {We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group $\{\rm Sym\}(\mathbb \{N\})$ as its additive group.},
author = {Ke, Wen-Fong, Meyer, Johannes H., Pilz, Günter F., Wendt, Gerhard},
journal = {Czechoslovak Mathematical Journal},
keywords = {infinite simple group; HNN extension; nearring with identity},
language = {eng},
number = {3},
pages = {869-880},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On zero-symmetric nearrings with identity whose additive groups are simple},
url = {http://eudml.org/doc/299296},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Ke, Wen-Fong
AU - Meyer, Johannes H.
AU - Pilz, Günter F.
AU - Wendt, Gerhard
TI - On zero-symmetric nearrings with identity whose additive groups are simple
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 869
EP - 880
AB - We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group ${\rm Sym}(\mathbb {N})$ as its additive group.
LA - eng
KW - infinite simple group; HNN extension; nearring with identity
UR - http://eudml.org/doc/299296
ER -

References

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