Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8055
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dc.contributor.authorPANJA, SAIKATen_US
dc.contributor.authorPrasad, Sachchidananden_US
dc.date.accessioned2023-06-26T03:56:27Z
dc.date.available2023-06-26T03:56:27Z
dc.date.issued2023-10en_US
dc.identifier.citationJournal of Algebra, 631, 148-193.en_US
dc.identifier.issn0021-8693en_US
dc.identifier.issn1090-266Xen_US
dc.identifier.urihttps://doi.org/10.1016/j.jalgebra.2023.04.027en_US
dc.identifier.urihttp://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8055
dc.description.abstractLet p be a polynomial in non-commutative variables x1, x2, ..., xn with constant term zero over an algebraically closed field K. The object of study in this paper is the image of this kind of polynomial over the algebra of upper triangular matri-ces Tm(K). We introduce a family of polynomials called multi-index p-inductive polynomials for a given polynomial p. Using this family we will show that, if p is a polynomial identity of Tt(K) but not of Tt+1(K), then p(Tm(K)) subset of Tm(K)(t-1). Equality is achieved in the case t = 1, m - 1 and an example has been provided to show that equality does not hold in gen-eral. We further prove existence of d such that each element of Tm(K)(t-1) can be written as sum of d many elements of p(Tm(K)). It has also been shown that the image ofTm(K)x under a word map is Zariski dense in Tm(K)x.(c)en_US
dc.language.isoenen_US
dc.publisherElsevier B.V.en_US
dc.subjectLvov-Kaplansky conjectureen_US
dc.subjectPolynomial mapsen_US
dc.subjectUpper triangular matrix algebraen_US
dc.subjectWord mapsen_US
dc.subjectUpper triangular matrix groupen_US
dc.subjectZariski topology2023-JUN-WEEK3en_US
dc.subjectTOC-JUN-2023en_US
dc.subject2023en_US
dc.titleThe image of polynomials and Waring type problems on upper triangular matrix algebrasen_US
dc.typeArticleen_US
dc.contributor.departmentDept. of Mathematicsen_US
dc.identifier.sourcetitleJournal of Algebraen_US
dc.publication.originofpublisherForeignen_US
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