On groups with cubic polynomial conditions
dc.contributor.author | Grishkov, A. [UNESP] | |
dc.contributor.author | Nunes, R. | |
dc.contributor.author | Sidki, S. | |
dc.contributor.institution | Universidade Estadual Paulista (UNESP) | |
dc.contributor.institution | Universidade Federal de Goiás (UFG) | |
dc.contributor.institution | Universidade de Brasília (UnB) | |
dc.date.accessioned | 2022-04-28T19:01:05Z | |
dc.date.available | 2022-04-28T19:01:05Z | |
dc.date.issued | 2015-09-01 | |
dc.description.abstract | Let F<inf>d</inf> be the free group of rank d, freely generated by {y1,. . .,yd}, and let DFd be the group ring over an integral domain D. Given a subset E<inf>d</inf> of F<inf>d</inf> containing the generating set, assign to each s in E<inf>d</inf> a monic polynomial ps(x)=xn+cs,n-1xn-1+. . .+cs,1x+cs,0∈D[x] and define the quotient ringA(d,n,Ed)=DFd〈ps(s)|s∈Ed〉ideal. When ps(s) is cubic for all s, we construct a finite set E<inf>d</inf> such that A(d,n,Ed) has finite rank over an extension of D by inverses of some of the coefficients of the polynomials. When the polynomials are all equal to (x-1)<sup>3</sup> and D=Z[16], we construct a finite subset P<inf>d</inf> of F<inf>d</inf> such that the quotient ring A(d,3,Pd) has finite D-rank and its augmentation ideal is nilpotent. The set P<inf>2</inf> is {y1,y2,y1y2,y1-1y2,y12y2,y1y22,[y1,y2]} and we prove that (x-1)3=0 is satisfied by all elements in the image of F<inf>2</inf> in A(2,3,Pd). | en |
dc.description.affiliation | Universidade Estadual de Sao Paulo | |
dc.description.affiliation | Universidade Federal de Goias | |
dc.description.affiliation | Departamento de Matemática, Universidade de Brasília | |
dc.description.affiliationUnesp | Universidade Estadual de Sao Paulo | |
dc.format.extent | 344-364 | |
dc.identifier | http://dx.doi.org/10.1016/j.jalgebra.2015.04.035 | |
dc.identifier.citation | Journal of Algebra, v. 437, p. 344-364. | |
dc.identifier.doi | 10.1016/j.jalgebra.2015.04.035 | |
dc.identifier.issn | 1090-266X | |
dc.identifier.issn | 0021-8693 | |
dc.identifier.scopus | 2-s2.0-84930181305 | |
dc.identifier.uri | http://hdl.handle.net/11449/220370 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | |
dc.source | Scopus | |
dc.subject | Cubic conditions on groups | |
dc.subject | Non-commutative Groebner | |
dc.subject | Unipotent groups | |
dc.title | On groups with cubic polynomial conditions | en |
dc.type | Artigo |