Minimal rings related to generalized quaternion rings

Grau, José María ; Oller-Marcén, Antonio M. (Universidad de Zaragoza) ; Szabo, Steve

Resumen: The family of rings of the form Z4 〈x, y〉〈x2 − a, y2 − b, yx − xy − 2(c + dx + ey + f xy)〉 is investigated which contains the generalized Hamilton quaternions over Z4. These rings are local rings of order 256. This family has 256 rings contained in 88 distinct isomorphism classes. Of the 88 non-isomorphic rings, 10 are minimal reversible nonsymmetric rings and 21 are minimal abelian reflexive nonsemicommutative rings. Few such examples have been identified in the literature thus far. The computational methods used to identify the isomorphism classes are also highlighted. Finally, some generalized Hamilton quaternion rings over Zps are characterized.

Idioma: Inglés

DOI: 10.24330/ieja.1281705

Año: 2023

Publicado en: International Electronic Journal of Algebra 34 (2023), [24 pp.]
ISSN: 1306-6048

Factor impacto SCIMAGO: 0.318 - Algebra and Number Theory (Q3)

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Didáctica Matemática (Dpto. Matemáticas)