000125765 001__ 125765 000125765 005__ 20240731103325.0 000125765 0247_ $$2doi$$a10.24330/ieja.1281705 000125765 0248_ $$2sideral$$a133308 000125765 037__ $$aART-2023-133308 000125765 041__ $$aeng 000125765 100__ $$aGrau, José María 000125765 245__ $$aMinimal rings related to generalized quaternion rings 000125765 260__ $$c2023 000125765 5060_ $$aAccess copy available to the general public$$fUnrestricted 000125765 5203_ $$aThe 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. 000125765 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000125765 592__ $$a0.318$$b2023 000125765 593__ $$aAlgebra and Number Theory$$c2023$$dQ3 000125765 594__ $$a0.9$$b2023 000125765 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000125765 700__ $$0(orcid)0000-0002-8191-3199$$aOller-Marcén, Antonio M.$$uUniversidad de Zaragoza 000125765 700__ $$aSzabo, Steve 000125765 7102_ $$12006$$2200$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Didáctica Matemática 000125765 773__ $$g34 (2023), [24 pp.]$$tInternational Electronic Journal of Algebra$$x1306-6048 000125765 8564_ $$s329578$$uhttps://zaguan.unizar.es/record/125765/files/texto_completo.pdf$$yVersión publicada 000125765 8564_ $$s1272668$$uhttps://zaguan.unizar.es/record/125765/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000125765 909CO $$ooai:zaguan.unizar.es:125765$$particulos$$pdriver 000125765 951__ $$a2024-07-31-09:44:29 000125765 980__ $$aARTICLE