Polynomials of degree 4 defining units

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorBroche, Osnel-
Autor(es): dc.creatordel Río, Ángel-
Data de aceite: dc.date.accessioned2026-02-09T12:54:42Z-
Data de disponibilização: dc.date.available2026-02-09T12:54:42Z-
Data de envio: dc.date.issued2019-08-29-
Data de envio: dc.date.issued2019-08-29-
Data de envio: dc.date.issued2017-
Fonte completa do material: dc.identifierhttps://repositorio.ufla.br/handle/1/36522-
Fonte completa do material: dc.identifierhttps://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=33&iss=4&rank=15&srch=searchterm%7CPolynomials+of+degree+4+defining+units-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1170747-
Descrição: dc.descriptionIf x is the generator of a cyclic group of order n then every element of the group ring Zx is the result of evaluating x at a polynomial of degree smaller than n with integral coefficients. When such an evaluation result into a unit we say that the polynomial defines a unit on order n. Marciniak and Sehgal have classified the polynomials of degree at most 3 defining units. The number of such polynomials is finite. However the number of polynomials of degree 4 defining units on order 5 is infinite and we give the full list of such polynomials. We prove that (up to a sign) every irreducible polynomial of degree 4 defining a unit on an order greater than 5 is of the form a(X4 + 1) + b(X3 + X) + (1 − 2a − 2b)X2 and obtain conditions for a polynomial of this form to define a unit. As an application we prove that if n is greater than 5 then the number of polynomials of degree 4 defining units on order n is finite and for n ≤ 10 we give explicitly all the polynomials of degree 4 defining units on order n. We also include a conjecture on what we expect to be the full list of polynomials of degree 4 defining units, which is based on computer aided calculations.-
Idioma: dc.languageen-
Publicador: dc.publisherEuropean Mathematical Society-
Direitos: dc.rightsrestrictAccess-
???dc.source???: dc.sourceRevista Matemática Iberoamericana-
Palavras-chave: dc.subjectGroup rings-
Palavras-chave: dc.subjectUnits-
Título: dc.titlePolynomials of degree 4 defining units-
Tipo de arquivo: dc.typeArtigo-
Aparece nas coleções:Repositório Institucional da Universidade Federal de Lavras (RIUFLA)

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