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On valuations of nearfields

Dalibor Klucký, Libuše Marková (1983)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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

Wen-Fong Ke, Johannes H. Meyer, Günter F. Pilz, Gerhard Wendt (2024)

Czechoslovak Mathematical Journal

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 ( ) as its additive group.

P ( r , m ) near-rings.

Balakrishnan, R., Suryanarayanan, S. (2000)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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